In this thesis we developed the new model kglobal for the purpose of studying nonthermal electron acceleration in macroscale magnetic reconnection. Unlike PIC codes we can simulate macroscale domains, and unlike MHD codes we can simulate particles that feedback onto the fluids so that the total energy of the system is conserved. This has never been done before. We have benchmarked the model by simulating Alfv\'en waves with electron pressure anisotropy, the growth of the firehose instability, and the growth of electron acoustic waves. We then studied the results of magnetic reconnection and found clear power-law tails that can extend for more than two decades in energy with a power-law index that decreases with the strength of the guide field. Reconnection in systems with guide fields approaching unity produce practically no nonthermal electrons. For weak guide fields the model is extremely efficient in producing nonthermal electrons. The nonthermals contain up to ~80% of the electron energy in our lowest guide field simulation. These results are generally consistent with flare observations and specifically the measurements of the September 10, 2017, flare.

Thermal conductivity and heat capacity have been established as powerful bulk probes for studying superconducting states which go beyond the standard BCS theory of superconductivity. In this thesis I present transport and thermodynamic measurements in ultra-low temperatures (down to 20 mK) on two different unconventional superconducting systems: AFe₂As₂ (A=K,Rb,Cs) and UTe₂.

In the first study, I present measurements of charge and thermal transport in the iron based superconductor KFe₂As₂ in magnetic fields aligned precisely in the ab-plane in order to study thermal transport in a Pauli limited superconductor with the quasiparticle mean free path controlled with disorder induced by electron irradiation. In KFe₂As₂ with a high level of disorder, a residual quasiparticle thermal conductivity which varies linearly in field is observed which is consistent with predictions for a paramagnetically limited superconductor. None of the measured samples display signatures of a first order superconducting transition or FFLO phase.

In the field induced normal state in a pristine sample of KFe₂As₂, we found non-Fermi liquid temperature dependence of the charge and thermal resistivity. Furthermore, the thermal resistivity indicates the persistence of strong inelastic quasiparticle scattering in the superconducting state for fields below H_c2. The resistivity was measured in fields up to 15 T along both the a and b axes in the pristine and irradited KFe₂As₂ samples as well as in RbFe₂As₂ and CsFe₂As₂. No indication of field tuning of the non-Fermi liquid behavior was observed. Instead, the field dependent resistivity in these samples follows a generalized Kohler scaling, indicating that the scattering mechanism giving rise to non-Femi liquid resistivity in zero field is unaffected by the application of magnetic field.

Finally, I present measurements of thermal transport and heat capacity in UTe₂ to resolve the superconducting gap structure. Surprisingly, no residual quasiparticle thermal conductivity is observed despite a large residual density of states observed in heat capacity. The rapid increase of residual quasiparticle thermal conductivity in magnetic field as well as the low temperature power law dependence of both heat capacity and magnetic penetration depth suggest a point nodal gap structure in UTe₂. Furthermore, careful measurements of the heat capacity in the vicinity of the superconducting transition uncover a splitting of the superconducting transition temperature indicative of two nearly degenerate superconducting phases present in UTe₂.

This dissertation describes energy dissipation and microwave loss due to non-equilibrium quasiparticles in superconducting transmon qubits and titanium nitride coplanar waveguide resonators. During the measurements of transmon  relaxation time and resonator quality factor , I observed reduced microwave loss as the temperature increased from 20 mK to approximately  at which the loss takes on a minimum value. I argue that this effect is due to non-equilibrium quasiparticles.

I measured the temperature dependence of the relaxation time  of the excited state of an Al/AlO_x/Al transmon and found that, in some cases,  increased by almost a factor of two as the temperature increased from 30 mK to 100 mK with a best  of 0.2 ms. I present an argument showing this unexpected temperature dependence occurs due to the behavior of non-equilibrium quasiparticles in devices in which one electrode in the tunnel junction has a smaller volume, and slightly smaller superconducting energy gap, than the other electrode. At sufficiently low temperatures, non-equilibrium quasiparticles accumulate in the electrode with the smaller gap, leading to a relatively high density of quasiparticles at the junction and a short . Increasing the temperature gives the quasiparticles enough thermal energy to occupy the higher gap electrode, reducing the density at the junction and increasing _. I present a model of this effect, extract the density of quasiparticles and the two superconducting energy gaps, and discuss implications for increasing the relaxation time of transmons.

I also observed a similar phenomenon in low temperature microwave studies of titanium nitride coplanar waveguide resonators. I report on loss in a resonator at temperatures from 20 mK up to 1.1 K and with the application of infrared pair breaking radiation ( ). With no applied IR light, the internal quality factor increased from  = 800,000 at T < 70 mK up to  at 600 mK. The resonant frequency  increased by 2 parts per million over the same temperature range. Above 600 mK both  and  decreased rapidly, consistent with the increase in the density of thermally generated quasiparticles. With the application of IR light and for intensities below  and T < 400 mK,  increased in a similar way to increasing the temperature before beginning to decrease with larger intensities. I show that a model involving non-equilibrium quasiparticles and two regions of different superconducting gaps can explain this unexpected behavior.

Anderson localization is a single particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity.

This increase results from a suppression of back scattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-1D Bose-Einstein condensates. We first describe back-scattering using a Fermi's golden rule approach, and then numerically confirm this picture by solving the time-dependent 1D Gross Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder.

We find that on the 10's of millisecond time scale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible back-scattering, while without SOC these same states rapidly localize.

Light does not typically scatter light, as witnessed by the linearity of Maxwell's equations. In this work, we demonstrate two superconducting circuits, in which microwave photons have well-defined energy and momentum, but their lifetime is finite due to decay into lower energy photons. The circuits we present are formed with Josephson junction arrays where strong quantum phase-slip fluctuations are present either in all of the junctions or in only a single junction. The quantum phase-slip fluctuations are shown to result in the strong inelastic photon-photon interaction observed in both circuits.

The phenomenon of a single photon decay provides a new way to study multiple long-standing many-body problems important for condensed matter physics. The examples of such problems, which we cover in this work include superconductor to insulator quantum phase transition in one dimension and a general quantum impurity problem. The photon lifetime data can be treated as a rare example of a verified and useful quantum many-body simulation.

This dissertation presents the first Deep-Neural-Network--based missing transverse momentum (pTmiss) estimator, called ``DeepMET''. It utilizes all reconstructed particles in an event as input, and assigns an individual weight to each of them. The DeepMET estimator is the negative of the vector sum of the weighted transverse momenta of all input particles. Compared with the pTmiss estimators currently utilized by the CMS Collaboration, DeepMET is found to improve the pTmiss resolution by 10-20%, and is more resilient towards the effect of additional proton-proton interactions accompanying the interaction of interest. DeepMET is demonstrated to improve the resolution on the recoil measurement of the W boson and reduce the systematic uncertainties on the W mass measurement by a large fraction compared with other pTmiss estimators.

The stellarator is a fusion energy concept that relies on fully three-dimensional shaping of magnetic fields to confine particles. Stellarators have many favorable properties, including, but not limited to, the ability to operate in steady-state, many optimizable degrees of freedom, and no strict upper limit on the plasma density. Due to the three-dimensional character of stellarators, theoretical and computational studies of stellarator physics are challenging and they possess some disadvantages compared to tokamaks. Namely, particle confinement and impurity control are problems in generic stellarator magnetic fields that must be addressed with optimized magnetic fields. Further, simulations will require a substantial increase in grid points because of the three-dimensional structure, leading to more expensive computations. This thesis will address both topics by first exploring the behavior of impurity particle transport in optimized stellarators, and then introducing a boundary condition to reduce the cost of stellarator turbulence simulations.

Impurity temperature screening is a favorable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields lead to intrinsically ambipolar neoclassical fluxes that give rise to temperature screening for low enough $\eta^{-1}\equiv d\ln n/d\ln T$. Here we examine the impurity particle flux in a number of approximately quasisymmetric stellarator configurations and parameter regimes while varying the amount of symmetry-breaking in the magnetic field. Results indicate that achieving temperature screening is possible, but unlikely, at low-collisionality reactor-relevant conditions in the core. A further look at the magnitude of these fluxes when compared to a gyro-Bohm turbulence estimate suggests that neoclassical fluxes are small in configurations optimized for quasisymmetry when compared to turbulent fluxes.

Calculating these turbulent fluxes is generally done by solving the gyrokinetic equation in a flux tube simulation domain, which employs coordinates aligned with the magnetic field lines. The standard ``twist-and-shift'' formulation of the boundary conditions \cite{Beer95} was derived assuming axisymmetry and is widely used because it is efficient, as long as the global magnetic shear is not too small. A generalization of this formulation is presented, appropriate for studies of non-axisymmetric, stellarator-symmetric configurations, as well as for axisymmetric configurations with small global shear. The key idea of this generalization is to rely on integrated local shear, allowing one significantly more freedom when choosing the extent of the simulation domain in each direction. Simulations of stellarator turbulence that employ the generalized parallel boundary conditions allow for lower resolution to be used compared to simulations that use the (incorrect, axisymmetric) standard parallel boundary condition.

Research at the intensity frontier of particle physics has led to the consideration of accelerators that push the limits on achievable beam intensities. At high beam intensities Coulomb interactions between charged particles generate a space charge force that complicates beam dynamics. The space charge force can lead to a range of nonlinear, intensity- limiting phenomena that result in degraded beam quality and current loss. This is the central issue faced by the next generation of high-intensity particle accelerators. An improved understanding of the interaction of the space charge forces and transverse particle motion will help researchers better design around these limiting issues. Furthermore, any scheme able to mitigate the impacts of such destructive interactions for space charge dominated beams would help alleviate a significant limitation in reaching higher beam intensities. Experimental work addressing these issues is presented using the University of Maryland Electron Ring (UMER).

This dissertation presents experimental studies of space charge dominated beams, and in particular the resonant interaction between the transverse motion of the beam and the periodic perturbations that occur due to the focusing elements in a circular ring. These interactions are characterized in terms of the tune shifts, Qx and Qy, that are the number of transverse oscillations (in and out of the plane of the ring) per trip around the ring. Resonances occur for both integer and half-integer values of tune shift. Particle tune measurement tools and resonance detection techniques are developed for use in the experiment. Results show no shift for either the integer (Qx = 7.0, Qy = 7.0) or half-integer (Qx = 6.5, Qy = 6.5) resonance bands as a function of space charge. Accepted theory predicts only a shift in the half-integer resonance case.

A second experiment testing the potential mitigation of transverse resonances through nonlinear detuning of particle orbits from resonance driving terms is also presented. The study included the design, simulation, and experimental test of a quasi-integrable accelerator lattice based on a single nonlinear octupole channel insert. Experiments measured a nonlinear amplitude dependent tune shift within the beam on the order of ∆Qx ≈ 0.02 and ∆Qy ≈ 0.03. The limited tolerances on accelerator steering prevented measuring any larger tune shifts.

The study of open physical systems concerns finding ways to incorporate the lack of information about the environment into a theory that best describes the behavior of the system. We consider characterizing the environment by using the system as a sensor, mitigating errors, and learning the physics governing systems out of equilibrium with computer algorithms.

We characterize long-range correlated errors and crosstalk, which are important factors that negatively impacts the performance of noisy intermediate-scale quantum (NISQ) computing devices. We propose a compressed sensing method for detecting correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s<<n(n-1)/2, and n is the total number of qubits). Our method uses entangled many-qubit GHZ states, and it can detect long-range correlations whose distribution is completely arbitrary, independent of the geometry of the system. Our method is also highly scalable: it requires only s log n measurement settings, and efficient classical postprocessing based on convex optimization.

To learn about physical systems using computer algorithms, we consider the problem of arrow of time. We show that a machine learning algorithm can learn to discern the direction of time's arrow when provided with a system's microscopic trajectory as input. Examination of the algorithm's decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be used to study systems out of equilibrium, and ultimately to uncover physical principles.

Topological photonics has opened new avenues to designing photonic devices along with opening a plethora of applications. Recently even though there have been many interesting studies in topological photonics in the classical domain, the quantum regime has remained largely unexplored. In this talk, I will speak on a recently developed a topological photonic crystal structure for interfacing single quantum dot spin with photon to realize light-matter interaction with topological photonic states. Developed on a thin slab of Gallium Arsenide(GaAs) membrane with electron beam lithography, such a device supports two robust counter-propagating edge states at the boundary of two distinct topological photonic crystals at near-IR wavelength. I will show the chiral coupling of circularly polarized lights emitted from a single Indium Arsenide(InAs) quantum dot under a strong magnetic field into these topological edge modes. Owing to the topological nature of these guided modes, I will demonstrate this photon routing to be robust against sharp corners along the waveguide.  Additionally, I will introduce a new topological component using valley-Hall topological photonic crystal and study the robustness in the system. This paves paths for fault-tolerant photonic circuits, secure quantum computation, exploring unconventional quantum states of light and chiral spin networks. 

Rydberg ensembles, atomic clouds with one or more atoms excited to a Rydberg state, have proven to be a good platform for the study of photon-photon interactions. This is due to the nonlinearities they exhibit at the single photon level arising from Rydberg-Rydberg interactions. As a result, they have shown promise for use in a multitude of applications, among them quantum networking.

In this thesis I describe the construction and operation of an apparatus for the purpose of cooling, trapping and probing Rydberg ensemble physics in a cloud of Rb 87 atoms. In addition, I describe a pair of projects undertaken with the apparatus. In the first, I report our demonstration of a Rydberg ensemble based on-demand single photon source. Here, we make use of Rydberg blockade to allow us to prepare a single collective Rydberg excitation in the cloud. The spin wave excitation is then retrieved by coherently mapping it onto a propagating photon. Our source is highly pure and efficient, while producing narrow bandwidth and indistinguishable photons.

Such sources are important devices for the purposes of quantum networking, computation and metrology. Following from this, I describe a collaborative project where we show time resolved Hong-Ou-Mandel interference between photons produced by our Rydberg ensemble source, and a collaborators source based on a single trapped barium ion. This demonstration is a critical step in the entanglement, and hybrid quantum networking, of these two disparate systems.

The Kuramoto model (KM) was initially proposed by Yoshiki Kuramoto in 1975 to model the dynamics of large populations of weakly coupled phase oscillators. Since then, the KM has proved to be a paradigmatic model, demonstrating dynamics that are complex enough to model a wide variety of nontrivial phenomena while remaining simple enough for detailed mathematical analyses. However, as a result of the mathematical simplifications in the construction of the model, the utility of the KM is somewhat restricted in its usual form. In this thesis we discuss extensions of the KM that allow it to be utilized in a wide variety of physical and biological problems.

First, we discuss an extension of the KM that describes the dynamics of theta neurons, i.e., quadratic-integrate-and-fire neurons. In particular, we study networks of such neurons and derive a mean-field description of the collective neuronal dynamics and the effects of different network topologies on these dynamics. This mean-field description is achieved via an analytic dimensionality reduction of the network dynamics that allows for an efficient characterization of the system attractors and their dependence not only on the degree distribution but also on the degree correlations.

Then, motivated by applications of the KM to the alignment of members in a two-dimensional swarm, we construct a Generalized Kuramoto Model (GKM) that extends the KM to arbitrary dimensions. Like the KM, the GKM in even dimensions continues to demonstrate a transition to coherence at a positive critical coupling strength. However, in odd dimensions the transition to coherence occurs discontinuously as the coupling strength is increased through 0.  In contrast to the unique stable incoherent equilibrium for the KM, we find that for even dimensions larger than 2 the GKM displays a continuum of different possible pretransition incoherent equilibria, each with distinct stability properties, leading to a novel phenomenon, which we call `Instability-Mediated Resetting.' To aid the analysis of such systems, we construct an exact dimensionality reduction technique with applicability to not only the GKM, but also other similar systems with high-dimensional agents beyond the GKM.

In the past few decades, research into electromagnetic properties of topological quantum materials has been one of the most active research areas in the field of condensed matter physics. Physicists have discovered a large class of materials, e.g. Weyl semimetals, topological insulators, and topological superconductors that can host a plethora of interesting topological properties. In addition to their theoretical value as novel and exotic phases of quantum matter, topological quantum materials provide a promising platform for an array of technological applications, particularly as building blocks of topological quantum computers. Unfortunately, despite great progress in the theoretical understanding of topological phases of matter, practical problems have made it difficult to: (i) identify unambiguous examples of topological quantum material and (ii) harness their potential for technological applications. The overarching goal of this thesis is to understand such difficulties and to find ways to overcome them by studying specific problems.

 This thesis is divided into four independent parts, each of which is dedicated to a particular problem: In the first part, we study chiral magnetic effect in Weyl semimetals and discuss whether it can be used to probe topological properties of Weyl semimetals in real experiments. In the second part, we propose an experimental setup to realize a certain type of topological excitation called  parafermionic zero mode using a quantum dot array structure from the 2/3 fractional quantum Hall state. Importantly, our proposal does not rely on Andreev backscattering. We argue that this feature makes our proposal suitable for experimental realization. In the third part, we provide a quantitative analysis of supercurrent in superconductor/quantum Hall/superconductor junctions and show that by making critical assumptions about the interface, it is possible to obtain a quantitative agreement between theory and the magnitude of the observed supercurrent. In the fourth part, we study quantum anomalous Hall effect and flavor ferromagnetism in twisted bilayer graphene and argue that the one-magnon spectrum can be used as a numerically accessible tool to study the stability of the quantum anomalous Hall phase in twisted bilayer graphene.

The transmission of extracellular information through intracellular signaling networks is ubiquitous in biology–-from single-celled organisms to complex multicellular systems. Via signal-transduction machinery, cells of all types can detect and respond to biological, chemical, and physical stimuli. Although studies of signaling mechanisms and pathways traditionally involve arrays of biochemical assays, detailed quantification of physical information is becoming an increasingly important tool for understanding the complexities of signaling. With the rich datasets currently being collected in biological experiments, understanding the mechanisms that govern intracellular signaling networks is becoming a multidisciplinary problem at the intersection of biology, computer science, physics, and applied mathematics.

In this dissertation, I focus on understanding and characterizing the physical behavior of signaling networks. Through analysis of experimental data, statistical modeling, and computational simulations, I explore a characteristic of signaling networks called excitability, and show that an excitable-systems framework is broadly applicable for explaining the connection between intracellular behaviors and cell functions.

One way to connect the physical behavior of signaling networks to cell function is through the structural and spatial analyses of signaling proteins. In the first part of this dissertation, I employ an adaptive-immune-cell model with a key activation step that is both promoted and inhibited by a microns-long, filamentous protein complex. In combining super-resolution images and a novel image-based bootstrap-like resampling method, I demonstrate that the spatial organization of signaling proteins is an important contributor to immune-cell self-regulation. To probe the excitable dynamics of the system, I develop a Monte Carlo simulation of nucleation-limited growth and degradation, and show that careful balance between simulation parameters can elicit a tunable response dynamic.

The spatiotemporal dynamics of signaling components are also important mediators of cell function. One key readout of the connection between signaling dynamics and cell function is the behavior of the cytoskeleton. In the second part of this dissertation, I use innate-immune-cell and epithelial-cell models to understand how a key cytoskeletal component, actin, is influenced by topographical features in the extracellular environment. Engineered nanotopographic substrates similar in size to typical extracellular-matrix structures have been shown to bias the flow of actin, a concept known as esotaxis. To measure this bias, I introduce a generalizable optical-flow-based-analysis suite that can robustly and systematically quantify the spatiotemporal dynamics of actin in both model systems. Interestingly, despite having wildly different migratory phenotypes and physiological functions, both cell types exhibit quantitatively similar topography-guidance dynamics which suggests that sensing and responding to extracellular textures is an evolutionarily conserved phenomenon.

The signaling mechanisms that enable actin responses to the physical environment are poorly understood. Despite experimental evidence for the enhancement of actin-nucleation-promoting factors (NPFs) on extracellular features, connecting texture-induced signaling to overall cell behavior is an ongoing challenge. In the third part of this dissertation, I study the topography-induced guidance of actin in amoeboid cells on nanotopographic textures of different spacings. Using optical-flow analysis and statistical modeling, I demonstrate that topography-induced guidance is strongest when the features are similar in size to typical actin-rich protrusions. To probe this mechanism further, I employ a dendritic-growth simulation of filament assembly and disassembly with realistic biochemical rates, NPFs, and filament-network-severing dynamics. These simulations demonstrate that topography-induced guidance is more likely the result of a redistribution, rather than an enhancement, of NPF components.

Overall, this dissertation introduces quantitative tools for the analysis, modeling, and simulations of excitable systems. I use these tools to demonstrate that an excitable-systems framework can provide deep, phenomenological insights into the character, organization, and dynamics of a variety of biological systems.

Superconducing Radio-Frequency (SRF) cavities are the backbone of a new generation of particle accelerators used by the High Energy Physics community. Nowadays, the applications of SRF cavities have expanded far beyond the needs of basic science. The proposed usages include waste treatment, water disinfection, material strengthening, medical applications and even use as high Q resonators in quantum computers. A practical SRF cavity needs to operate at extremely high rf fields while remaining in the low-loss superconducting state. State of the art Nb cavities can easily reach quality factors Q > 2 × 10¹⁰ at 1.3 GHz.

Currently, the performance of the SRF cavities is limited by surface defects which lead to cavity breakdown at high accelerating gradients. Also, there are efforts to reduce the cost of manufacturing SRF cavities, and the cost of operation. This will require an R&D effort to go beyond bulk Nb cavities. Alternatives to bulk Nb are Nb-coated Copper and Nb₃Sn cavities. When a new SRF surface treatment, coating technique, or surface optimization method is being tested, it is usually very costly and time consuming to fabricate a full cavity. A rapid rf characterization technique is needed to identify deleterious defects on Nb surfaces and to compare the surface response of materials fabricated by different surface treatments. In this thesis a local rf characterization technique that could fulfill this requirement is presented.

First, a Scanning Magnetic Microwave Microscopy technique was used to study SRF grade Nb samples. Using this novel microscope the existence of surface weak-links was confirmed through their local nonlinear response. Time-Dependent Ginzburg-Landau (TDGL) simulations were used to reveal that vortex semiloops are created by the inhomogenious magnetic field of the magnetic probe, and contribute to the measured response.

Also, a system was put in place to measure the surface resistance of SRF cavities at extremely low temperatures, down to T = 70 mK, where the predictions for the surface resistance from various theoretical models diverge. SRF cavities require special treatment during the cooldown and measurement. This includes cooling the cavity down at a rate greater than 1K/minute, and very low ambient magnetic field B < 50 nT. I present solutions to both of these challenges.

In this dissertation, unconventional superconducting systems, such as superconductors with non s-wave pairing symmetry and superconductors with non-trivial topology, are investigated by means of microwave experimental techniques. The thesis consists of two parts. Part 1 of the thesis will discuss a newly developed microwave superconducting gap spectroscopy system. Using a combination of the resonant microwave transmission technique and laser scanning microscopy, it is demonstrated that the new technique can directly image the pairing symmetry of superconductors with unconventional pairing symmetries. During the demonstration with an example d-wave superconductor, a signature of Andreev bound states was also found. A phenomenological model to explain the observed properties of the Andreev bound states is also discussed and compared to data. Lastly, an effort to broaden the applicability of the new technique to samples of more general morphology is discussed.

Part 2 of the thesis will introduce the microwave surface impedance technique and its application to the characterization of topological superconducting systems. A thickness dependent surface reactance study of an artificial topological superconductor SmB₆/YB₆ (topological insulator / superconductor bilayer) was used to determine the characteristic lengths of the system (normal coherence length, penetration depth, and thickness of the topological surface state), and revealed robust bulk insulating properties of the SmB₆ thin films. A surface resistance and reactance study on the candidate intrinsic topological superconductor UTe₂ revealed the existence of residual normal fluid and a chiral spin-triplet pairing state, which together point out the possible existence of an itinerant Majorana normal fluid on the surface of chiral superconductors. 

Future measurements of primordial non-Gaussianity (NG) can reveal the mass and the spin information of cosmologically produced particles with masses of order the inflationary Hubble scale, H_inf, which can be as high as 10^13 GeV. In this talk, I will describe how such NG measurements can be used as an on-shell probe of, a) Grand Unified Theories and, b) low scale gauge theories that get “heavy-lifted” to ~ H_inf scales. I will also discuss a simple alternative to the standard inflationary paradigm, involving a curvaton field, that can allow NG signals orders of magnitude larger compared to standard inflation. This brings various motivated particle physics signatures, such as loops of heavy gauge-charged scalars and fermions, within future observational reach.

Quasi one-dimensional (1D) clouds of ultracold atoms are an ideal platform for quantum simulation and experimental benchmarking of simple 1D physics. I present two experiments with elongated clouds of ultracold alkali Rb-87 in two different 1D regimes, where optical microscopy comprises measurement. In a first experiment, we probe the thermodynamics of individual, strongly interacting 1D Bose gases by measuring their equations of state in-situ. In a second experiment with weakly interacting elongated condensates, we apply digital holographic microscopy to transfer hardware complexity into software by removing the effects of aberrations in our resonant absorption images.

Intense laser-plasma interactions, generally characterized by focused laser intensities exceeding several TW per cm², are of basic and applied interest in a number of areas, , including the generation of relativistic charged particle beams, high energy photon generation, and nonlinear optics extending to the relativistic regime . Mid-infrared (mid-IR) lasers provide favorable wavelength scaling of various laser-plasma interaction parameters compared to commonly used near-infrared systems, and in several cases enable entirely new phenomena. In this dissertation we present experimental and computational results relating to three laser-plasma based applications using ultrashort mid-infrared and long-wave-infrared laser pulses. First, we demonstrate self-modulated laser wakefield acceleration driven by mid-IR laser pulses collapsing in near-critical density targets, and discuss scaling from common near-infrared systems. Second, we demonstrate that electron avalanche breakdown driven by picosecond, mid-IR lasers drive discrete breakdowns from individual seed electrons, providing a unique and extremely sensitive method of detecting ultralow plasma densities in gases. We apply this technique to demonstrate standoff detection of radioactive materials, and to measure laser ionization yield in atmospheric pressure range gases over an unprecedented 14 orders of magnitude. Finally, we present a theory of self-guiding for high power mid-infrared and long-wave-infrared multi-picosecond pulses interacting with discrete avalanche breakdown sites, and show through propagation simulations that aerosol-initiated avalanches support self-guiding at moderate intensities.

In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly collisional plasma is challenging. The equation system of relevance, the Vlasov-Maxwell-Fokker-Planck (VM-FP) system of equations, is difficult to numerically integrate, and traditional methods such as the particle-in-cell method introduce counting noise into the distribution function. 

In this final public examination, we present a new algorithm for the discretization of VM-FP system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin (DG) finite element method for the spatial discretization and a third order strong-stability preserving Runge--Kutta for the time discretization, we obtain an accurate solution for the plasma's distribution function in space and time. 

We both prove the numerical method retains key physical properties of the VM-FP system, such as the conservation of energy and the second law of thermodynamics, and demonstrate these properties numerically. These results are contextualized in the history of the DG method. We discuss the importance of the algorithm being alias-free, a necessary condition for deriving stable DG schemes of kinetic equations so as to retain the implicit conservation relations embedded in the particle distribution function, and the computational favorable implementation using a modal, orthonormal basis in comparison to traditional DG methods applied in computational fluid dynamics. 

A diverse array of simulations are performed which exploit the advantages of our approach over competing numerical methods. We demonstrate how the high fidelity representation of the distribution function, combined with novel diagnostics, permits detailed analysis of the energization mechanisms in fundamental plasma processes such as collisionless shocks. Likewise, we show the undesirable effect particle noise can have on both solution quality, and ease of analysis, with a study of kinetic instabilities with both our continuum VM-FP method and a particle-in-cell method.

Our VM-FP solver is implemented in the Gkeyll framework (https://github.com/ammarhakim/gkyl), a modular framework for the solution to a variety of equation systems in plasma physics and fluid dynamics.

Laser wakefield electron accelerators (LWFAs) can support accelerating gradients three orders of magnitude higher than conventional radio frequency linear accelerators, enabling compact laser-driven devices. In this dissertation, I explore two regimes of LWFA physics, one at high plasma density, and the other at low density.

The first part of this thesis characterizes bright broadband coherent radiation emitted during wakefield acceleration driven by femtosecond laser interaction with high, near-critical density plasma. Detailed measurement is presented of the radiation spectrum, polarization and angular distribution. The results are consistent with synchrotron radiation emission from laser-assisted injection into wakefields, with this picture supported by particle-in-cell simulations.

The second part of this thesis demonstrates the use of high intensity Bessel beams of various orders for generating low density plasma waveguides that guide high intensity laser pulses over tens of centimeters.  Methods are presented for Bessel beam generation and focus optimization using adaptive optics.

Quantum computing promises solutions to some of the world's most important problems that classical computers have failed to address. The trapped-ion-based quantum computing platform has a lot of advantages for doing so: ions are perfectly identical and near-perfectly isolated, feature long coherent times, and allow high-fidelity individual laser-controlled operations. One of the greatest remaining obstacles in trapped-ion-based quantum computing is the issue of scalability. The approach that we take to address this issue is a modular architecture: separate ion traps, each with a manageable number of ions, are interconnected via photonic links. To avoid photon-generated crosstalk between qubits and utilize advantages of different kinds of ions for each role, we use two distinct species -- 171Yb+ as memory qubits and 138Ba+ as communication qubits. The qubits based on 171Yb+ are defined within the hyperfine “clock” states characterized by a very long coherence time while 138Ba+ ions feature visible-range wavelength emission lines. Current optical and fiber technologies are more efficient in this range than at shorter wavelengths.

We present a theoretical description and experimental demonstration of the key elements of a quantum network based on the mixed-species paradigm. The first one is entanglement between an atomic qubit and the polarization degree of freedom of a pure single photon. To verify the purity of single photons, we measure the second-order correlation function and find g(2)(0)=(8.1±2.3)×10-5 without background subtraction, which is consistent with the lowest reported value in any system. Next, we show mixed-species entangling gates with two ions using the Mølmer-Sørensen and Cirac-Zoller protocols. Finally, we theoretically generalize mixed-species entangling gates to long ion chains and characterize the roles of normal modes there. In addition, we explore sympathetic cooling efficiency in such mixed-species crystals. Besides these developments, we demonstrate new techniques for manipulating states within the D3/2-manifold of zero-nuclear-spin ions -- a part of a protected qubit scheme promising seconds-long coherence times proposed by Aharon et al. in 2013.

Topological phases are intriguing phases of matter which cannot be described with traditional theories of the phase transition such as Ginzburg-Landau theory, and numerous efforts has been put to achieve these exotic phases of matter in a variety of quantum platforms. In this thesis, we discuss how topological quantum states of matter can be engineered by utilizing spatially patterned light, which has become available thanks to the recent advances in beam shaping techniques.

First, we discuss a scheme to construct an optical lattice to confine ultracold atoms on the surface of torus. We investigate the feasibility of this construction with numerical calculations as well as propose a supercurrent generation experiment to verify the non-trivial topology of the created surface. We also propose a scheme to construct fractional quantum Hall states which can demonstrate topological degeneracy. We then extend our effort for creation of topologically non-trivial surfaces for ultracold atoms to the surfaces with open boundaries, using a bilayer optical lattice with multiple pairs of twist defects. We explain how a spin-dependent optical lattice can serve as the bilayer optical lattice for this purpose as well as the scheme for preparing and optically manipulating the fractional quantum Hall states.

Then we turn our attention to driven electronic systems. In particular, we investigate a way to imprint the superlattice structure in two-dimensional electronic systems by shining circularly-polarized light. We demonstrate the wide optical tunability of this system allows to a variety of band properties. We show that these tunable band properties lead to exotic physics ranging from the topological transitions to the creation of nearly flat bands, which can allow a realization of strongly correlated phenomena in Floquet systems. We then investigate the Floqut vortex states created by shining light carrying non-zero orbital angular momentum on a 2D semiconductor. We analytically and numerically study the properties of those vortex states and show that such Floquet vortex states exhibit a wide range of tunability and illustrate the potential utility of such tunability with an example of application in quantum state engineering.

Granular matter is a broad term that describes materials comprised of macroscopic grains. Granular material has unique properties that can mimic either a solid- or fluid-like system and has macroscopic behaviors such as segregation, shear- jamming, reversibility, and compaction. The finite size of the grains implies that tools developed in thermodynamics cannot be readily applied. Instead, research into granular material uses a combination of bulk measurements (density, pressure) with grain-scale tracking of position, orientation, and forces. This thesis presents four main studies utilizing three-dimensional experiments and simulations to probe the dynamics of individual grain subject to cyclic compression.

The first study uses numerical simulations to connect granular rotations to translations in sheared granular packings. It is proposed that rotations play an extensive roll in the formation of shear zones in granular packing, in which the rotations allow for ball-bearing like motion that could reduce the stress from external pressures. In this study, we quantify the effect of friction on the shear-zone rotations and translations. We find a direct connection between average rotations and the vorticity of translations independent of the friction. The second study explores reversibility of grain translations and rotations in the context of memory formation. In granular matter, memory is formed via a response to an external perturbation, ranging from compression and shear to thermal cycling. In this project, we encode and readout memory of compression amplitudes for a cyclically driven granular system. We find that memory is significantly affected by the inter particle friction of each grain and is most readily extracted by quantifying reversible displacements within the sample.

The third study experimentally measures three-dimensional orientations of granular spheres using our refractive index matched scanning setup. We apply a combination of deep learning and image processing to extract the position and orientation of individual grains subject to cyclic compression. Using this, we can quantify the spatial distribution of sliding and rolling motion of contacts. We find that sliding occur deep within the sample where the grains are mostly fixed in place. This occurs with an increase in internal stress within the material.

Finally, we explore collectively rotating states in three-dimensions. We introduce a new measure in which we can identify affine (collective) and non-affine rotations. We find that grain rotations are generated by minimizing sliding motion between all contacts independent of the forces between each contact. Further, we find that the affine component is more directly correlated to irreversible translations than the non-affine. This result identifies that collective rotations are important to reversible states in sheared granular systems.

The quality of modern astrophysical spectra has made it clear that there is a lack of sufficiently accurate and robust laboratory atomic reference data sets. Particularly for spectra of the iron-group elements, the growing demand for critically evaluated sets of comprehensive atomic data is a direct result of advancing stellar astrophysics models and fundamental physics problems probing beyond the standard model. My thesis reports on my critical evaluation of the Ni V spectrum and the recent laboratory measurements I have conducted to improve the state of available reference data for astrophysical applications that rely on observations of Ni V. Additionally, I report my laboratory measurements of Fe II branching fraction values in the UV/VUV.

Using high-resolution grating spectroscopy at the National Institute of Standards and Technology, I carried out an analysis of quadruply ionized iron and nickel (Fe V & Ni V) in the vacuum ultraviolet (VUV) region by both recording new spectra and critically evaluating previously published data sets. My analysis resulted in highly accurate wavelengths, presented with calculated oscillator strengths, for roughly 1500 Ni V lines, 200 of which have uncertainties that are almost an order of magnitude lower than in previous publications. Additionally, I present over 300 Ni V energy levels derived from my evaluated wavelengths. My work also strongly supports the previous evaluations of Fe V by another author. With the extreme accuracy requirements of modern astrophysics problems, confirming the wavelength scale and uncertainty evaluation of previous Fe V data sets is still significant.

Additionally my thesis also presents measurements of singly ionized iron (Fe II) branching fractions (BFs) in the VUV using high-resolution Fourier-transform spectroscopy. BFs are essential values for interpreting complex astrophysical spectra, but are notoriously difficult to measure in the VUV; for this reason, VUV BFs of Fe II have only been reported by one other research group for just seven levels. My thesis reports accurate BFs for 10 Fe II levels, involving approximately 150 spectral lines, which roughly doubles the amount of reported Fe II BFs in UV/VUV.

Studying topological states of matter offers potential routes to novel excitations with properties beyond that of simple electrons. While the range of materials and techniques for studying topological systems is constantly expanding, only a handful of systems have been thoroughly studied. Topological crystalline insulators (TCI) and the rich states present in ZrTe5 offer alternative routes to studying topological states of matter with surface states of distinct character to those in more common 3d topological insulators.

First, we report on the fabrication of Josephson junctions using MBE-grown candidate TCI material — Pb-doped SnTe — as weak links.  We then perform transport characterization measurements on these devices including the effects of DC, RF, and magnetic field biases. Finally, we model these results using a skewed current phase relationship using the resistively shunted josephson junction model.  

In the second section, we present the fabrication of devices from mechanically exfoliated ZrTe5 nanowires. After fabrication, we perform magnetoconductance measurements at various temperatures for these devices.  We then use existing models for weak antilocalization and universal conductance fluctuations for a quasi-1D system in order to extract a coherence length for this system.  

Due to their high degree of controllability and precise measurement capabilities, ultracold ensembles of neutral atoms have emerged as a promising platform for performing quantum simulations. In this thesis, I will describe the design and construction of an analog quantum simulator based on $^{23}$Na Bose-Einstein Condensates (BEC). Our system can produce and trap BECs in arbitrary-shaped quasi two-dimensional optical dipole traps, which can be dynamically altered during an experimental sequence. Such controlled variation of the BEC's spatial mode enables exploration of open questions in superfluidity, atomtronics, and analogue cosmology. I will describe the implementation of our system to study the inflationary dynamics of the early universe and report our recent results on the simulation of Cosmological Hubble friction. We expand and contract a toroidally shaped BEC and analyze the time evolution of its collective phonon modes. These excitations are analogous to fluctuating scalar fields in an expanding universe. The changing metric of the expanding or contracting background BEC results in dilation of the phonon field through a term dependent on the expansion speed, similar to Hubble friction in inflationary models of the universe. We conclusively demonstrate the analogy by experimentally measuring Hubble attenuation and amplification. Our measured strength of Hubble friction disagrees with recent theoretical work [J. M. Gomez Llorente and J. Plata, Phys. Rev. A 100 043613 (2019) and S. Eckel and T. Jacobson, SciPost Phys. 10 64 (2021)], suggesting inadequacies in the current model.

A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. Here, we experimentally investigate three such cases.

In the first part of the thesis, we fabricate JJs with weak links made of the topological crystalline insulator PbSnTe, and additional JJs with weak links made of its topologically trivial cousin, PbTe. In characterizing these junctions, we find that measurements of the AC Josephson effect reveal a stark difference between the two: while the PbTe JJs exhibit Shapiro steps at the expected values of V=nhf/2e, PbSnTe JJs show more complicated subharmonic structure. We present the skewed sinusoidal CPR necessary to reproduce these measurements, and discuss this alteration to the CPR as a consequence of 1D helical channels arising from the topologically nontrivial surface state.

In the second part of the thesis, we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in Josephson junctions. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These observations include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. We analyze how multiband effects and the experimentally visualized ferroelectric domain walls may give rise to a nonstandard CPR, giving insight into the Josephson effect in materials that possess ferroelectricity and/or multiband superconductivity.

Finally, we fabricate and measure JJs with weak links made of the topological insulator (BiSb)₂Te₃. Under low frequency RF radiation, we observe suppression of the first and third Shapiro steps, consistent with the fractional AC Josephson effect. This could indicate a signature of 4π periodicity in the junction's CPR, which may in turn suggest the presence of Majorana bound states. However, not all of our measured devices confirm this observation, as some of them show suppression of only the first step, while still others show probabilistic distortions to the AC Josephson effect which might indicate other nonequilibrium effects at play. We discuss the inconsistency of our measurements with topologically trivial sources of step suppression that have been suggested in the literature.

Multipole transitions beyond the dipole approximation apply when the Bohr radius of the quantum state is larger or comparable to the excitation wavelength. This is rarely the case for atoms or quantum dots. However, in the quantum Hall regime, wave functions can be extended to a length scale comparable to optical wavelengths, and the coherence is topologically protected against dephasing. Consequently, multipole transitions become possible. Motivated by this, we study the light-matter interaction in graphene in the quantum Hall regime, manifested as the photocurrent (PC).

In the first part of the thesis, we experimentally study the PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples’ edges are observed with minimal obscurations and noise. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs’ power dependence and their saturation behavior.  We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical-phonons and Coulomb interactions.  The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication.

In the second part, we theoretically study the light-matter interaction beyond dipole, manifested as a PC. Inspired by the seminal gedankenexperiment by Laughlin which describes the charge transport in quantum Hall systems via the pumping of flux, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbital angular momentum interacts with electronic Landau levels, it acts as a flux pump which radially moves the electrons through the sample. We investigate this effect for a graphene system with Corbino geometry, and calculate the radial current in the absence of any electric potential bias. Remarkably, the current is robust against the disorder, and in the weak excitation limit, the current shows a power-law scaling with intensity characterized by the novel exponent 2/3.

Laser wakefield accelerators (LWFA) can support acceleration gradients orders of magnitude higher than conventional radio frequency linear accelerators.  This gives them the potential to drive the next generation of accelerators for high energy physics, as well as compact accelerators for many other applications.  However, in order to reach higher energies and improve electron beam quality, LWFA requires the development of plasma waveguides.

This thesis demonstrates two new all optical techniques for the creation of plasma waveguides.  The first, “two-Bessel” technique uses a  Bessel beam to form the core of the waveguide and a higher order  Bessel beam to form the cladding.  In the second, “self-waveguiding” technique, the guided beam itself forms the cladding of the waveguide.  Preliminary electron acceleration results using the self-guiding technique, as well electron acceleration simulations are also presented. 

Neutrinos are the most mysterious particles in the standard model. Many of their fundamental properties such as their masses, lifetimes, and nature (Dirac or Majorana) are yet to be pinned down by experiments. Currently, the strongest bound on neutrino masses comes from cosmology. This bound is obtained by scrutinizing the gravitational effect of the cosmic neutrinos on the evolution of structure in our universe. However, this bound assumes that the neutrinos from the Big Bang have survived until the present day. In this dissertation, the unstable neutrino scenario is studied in light of current and near-future cosmological experiments. We show that the current cosmological bound on the neutrino masses can be relaxed significantly in an unstable neutrino scenario. We further show that near-future experiments offer the possibility of independently measuring both the masses of the neutrinos and their lifetimes.

We consider an elusive scenario in which the cosmic neutrinos decay into invisible radiation after becoming non-relativistic. The Boltzmann equations that govern the cosmological evolution of density perturbations in the case of unstable neutrinos are derived and solved numerically to determine the effects on the matter power spectrum and lensing of the cosmic microwave background (CMB). A Markov-Chain Monte-Carlo (MCMC) analysis is done on the current cosmological data and mock future data to obtain its sensitivity to the neutrino masses and lifetimes. We show that the effect of the neutrino masses on large scale structure is dampened by the decay of neutrinos, which leads to a parameter degeneracy between the neutrino masses and lifetimes inferred from the cosmological data. This degeneracy allows a significant relaxation of the current cosmological upper bound on the sum of neutrino masses from about 0.2 eV in the stable neutrino case to 0.9 eV in the unstable neutrino scenario. This window is important for terrestrial experiments such as KATRIN which are seeking to independently measure the neutrino masses in the laboratory. We further show that near-future large scale structure measurements from the Euclid satellite, when combined with cosmic microwave background data from Planck, may allow an independent determination of both the lifetimes of the neutrinos and the sum of their masses. These parameters can be independently determined because the Euclid data will cover a range of redshifts, allowing the growth of structure over time to be tracked. If neutrinos are stable on cosmological timescales, we show that these observations can improve the lower limit on the lifetimes of the neutrinos by seven orders of magnitude, from O(10) years to 2 x 10^8 years (95 % C.L.), without significantly affecting the measurement of the neutrino masses. On the other hand, if neutrinos decay after becoming non-relativistic but on timescales less than O(100) million years, these observations may allow, not just the first measurement of the sum of neutrino masses, but also the determination of the neutrino lifetime from cosmology.

Quantum computers have come a long way since conception, and there is still a long way to go before the dream of universal, fault-tolerant computation is realized. In the near term, quantum computers will occupy a middle ground that is popularly known as the “Noisy, Intermediate-Scale Quantum” (or NISQ) regime. The NISQ era represents a transition in the nature of quantum devices from experimental to computational. There is significant interest in engineering NISQ devices and NISQ algorithms in a manner that will guide the development of quantum computation in this regime and into the era of fault-tolerant quantum computing.

In this thesis, we study two aspects of near-term quantum computation. The first of these is the design of device architectures, covered in Chapters 2, 3, and 4. We examine different qubit connectivities on the basis of their graph properties, and present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and graphs with modular structure. Next, we discuss the problem of permuting qubits among the nodes of the connectivity graph using only local operations, also known as routing. Using a fast quantum primitive to reverse the qubits in a chain, we construct a hybrid, quantum/classical routing algorithm on the chain. We show via rigorous bounds that this approach is faster than any SWAP-based algorithm for the same problem.

The second part, which spans the final three chapters, discusses variational algorithms, which are a class of algorithms particular suited to near-term quantum computation. Two prototypical variational algorithms, quantum adiabatic optimization (QAO) and the quantum approximate optimization algorithm (QAOA), are studied for the difference in their control strategies. We show that on certain crafted problem instances, bang-bang control (QAOA) can be as much as exponentially faster than quasistatic control (QAO). Next, we demonstrate the performance of variational state preparation on an analog quantum simulator based on trapped ions. We show that using classical heuristics that exploit structure in the variational parameter landscape, one can find circuit parameters efficiently in system size as well as circuit depth. In the experiment, we approximate the ground state of a critical Ising model with long-ranged interactions on up to 40 spins. 

Finally, we study the performance of Local Tensor, a classical heuristic algorithm inspired by QAOA on benchmarking instances of the MaxCut problem, and suggest physically motivated choices for the algorithm hyperparameters that are found to perform well empirically. We also show that our implementation of Local Tensor mimics imaginary-time quantum evolution under the problem Hamiltonian.

Besides potentially delivering a huge leap in computational power, quantum computers also offer an essential platform for simulating properties of quantum systems.  Consequently, various algorithms have been developed for approximating the dynamics of a target system on quantum computers. But generic quantum simulation algorithms---developed to simulate all Hamiltonians---are unlikely to result in optimal simulations of most physically relevant systems; optimal quantum algorithms need to exploit unique properties of target systems.

The aim of this dissertation is to study two prominent properties of physical systems, namely locality and symmetry, and subsequently leverage these properties to design efficient quantum simulation algorithms.

In the first part of the dissertation, we explore the locality of quantum systems and the fundamental limits on the propagation of information in power-law interacting systems. We prove upper limits on the speed at which information can propagate in power-law systems. We also demonstrate how such speed limits can be achieved by protocols for transferring quantum information and generating quantum entanglement. We then use these speed limits to constrain the propagation of error and improve the performance of digital quantum simulation. Additionally, we consider the implications of the speed limits on entanglement generation, the dynamics of correlation, the heating time, and the scrambling time in power-law interacting systems.

In the second part of the dissertation, we propose a scheme to leverage the symmetry of target systems to suppress error in digital quantum simulation. We first study a phenomenon called destructive error interference, where the errors from different steps of a simulation cancel out each other. We then show that one can induce the destructive error interference by interweaving the simulation with unitary transformations generated by the symmetry of the target system, effectively providing a faster quantum simulation by symmetry protection. We also derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection.

In recent decades, the rapid development of quantum technologies has led to a new era of programmable platforms, enabling the realizations of quantum simulation and quantum computation. This dissertation is motivated by recent experimental progress on controlling individual quantum degrees of freedom in systems such as trapped ions and Rydberg atom arrays.  By tailoring the interactions in these quantum systems, we study analog quantum simulations of various physical phenomena, including non-equilibrium quantum dynamics and nontrivial topological physics.

In the first part of the dissertation, we study slow quantum many-body dynamics in trapped-ion systems and Rydberg atom arrays. We first show that either the long-range interactions or an additional symmetry-breaking field can give rise to a confining potential. Such a potential can couple domain wall quasiparticles into mesonic or baryonic bound states.  These confined quasiparticles strongly suppress the quantum information dynamics and lead to slow thermalization.  In the limit of strict domain-wall confinement, the full Hilbert space is fragmented into exponentially many disconnected subspaces. Further, we demonstrate that thermalization can be halted by quantum engineering a uniformly increasing field in the trapped-ion quantum simulator.

The second part of the dissertation focuses on topologically relevant phenomena in quantum simulators. We first study the effect of experimentally relevant disorder in 2D Rydberg atom arrays. We find that there are three distinct localization regimes due to the presence of nontrivial topological bands. We further study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We show that the interplay of anyonic statistics and interactions can give rise to spatially asymmetric quantum dynamics. Finally, we use Nielsen's geometric approach to quantify the circuit complexity in topological models. We find that circuit complexity of ground states and circuit complexity of non-equilibrium steady states both exhibit nonanalytical behavior at topological transition points.

I will discuss the cosmological (de)confinement phase transition (PT) of nearly conformal, strongly coupled large N field theories, applicable to composite Higgs models, using their holographic dual 5D formulation.  In this description, the PT is from the high temperature phase in which the IR of the warped extra dimension is covered by a black-brane horizon to the low temperature Randall-Sundrum-1 phase. The PT proceeds by percolation of IR-brane bubbles nucleating from the horizon, and the bubble dynamics during the PT sources a stochastic gravitational wave background that can be detected by future experiments. I will show how to construct a smooth configuration that interpolates between the two phases, allowing for a controlled description of bubble nucleation within 5D EFT. We will see that the cosmological PT in the minimal models can complete only after a large period of supercooling, potentially resulting in excessive dilution of primordial matter abundances. I will then show how generic modifications of the minimal models can result in a much faster completion of the PT. Finally, I will discuss the gravitational wave signal produced by the PT and the implications of the PT for baryogenesis.

Quantum computers have wide-ranging potential applications, many of which will require thousands or even millions of quantum bits to be useful. Current state-of-the-art universal quantum computers, on the other hand, contain only several tens of qubits, and scaling to larger system sizes remains one of the primary challenges. Among current quantum computing platforms, trapped ions are a leading hardware option. One proposal for scaling such systems consists of a modular architecture.

The architecture consists of multiple nodes, each with an ion trap containing a communication qubit (¹³⁸Ba⁺) and a memory qubit (¹⁷¹Yb⁺). The communication qubit is responsible for generating photons that link the remote nodes together via entanglement swapping while the memory qubits are used for storing information and performing local computations. We report progress towards demonstration of the remote entanglement of two barium ions. The creation of this link is a probabilistic process and fails much more often than it succeeds. The success rate does not impact the fidelity of the resulting entangled state but imposes significant constraints on the utility of this protocol. We examine the current limitations on both the fidelity of the resulting entangled state and the success probability.

In addition to the two-node experiment, we have designed and built a new ion trap system that should yield much higher photon collection rates. This design represents a significant shift from previous systems because of the inclusion of optical elements inside the vacuum chamber and their resulting proximity to the ions. We incorporate two objective lenses with a numerical aperture of 0.8, each of which can collect twice as much light as the objectives used for the remote entanglement experiment. We present preliminary results characterizing the performance of this system and discuss how it could be incorporated into a three-node network, which has not yet been demonstrated using trapped ions.

GRBs have long been considered as potential sources of hadronic acceleration of ultra-high energy cosmic rays and, more recently, as potential sources of the diffuse neutrino flux measured by IceCube. This thesis presents a search for neutrinos correlated with 2,091 gamma-ray bursts (GRBs) in prompt and extended time windows using data from the IceCube Neutrino Observatory ranging from May 2011 to October 2018. Ten time windows, ranging from 10 seconds to -1/+14 days around the time of the GRB's gamma-ray emission, were searched for coincident neutrino emission and a p-value was assigned based on the most significant time window. The results for all 2,091 GRBs were divided by region of the sky and observed gamma-ray emission time, and were evaluated with a Binomial test, which was found to be consistent with background. The 23 most significant GRBs were examined in more detail and they were also found to be consistent with background. Limits were set assuming two flux models: equal neutrino flux at Earth for every GRB and standard candle neutrino emission. The equal flux at Earth model led to similar constraints as previous IceCube prompt GRB studies, namely that GRBs are responsible for, at most, a few percent of the diffuse flux. The results of the standard candle analysis, however, indicate GRBs may be contributing up to 11% of the diffuse neutrino flux up to 1,000 second timescales, which leaves the door open to GRBs as neutrino sources and hadronic accelerators of at least some of the ultra-high energy cosmic rays.

Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are intractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates.

To increase the system size, we report on the design, construction, and operation of an integrated trapped ion quantum computer consisting of a chain of 15 ¹⁷¹Yb⁺ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that accurately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions throughout a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment.

One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state.  These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it.

Dissertation Title: Simulating many-body quantum spin models with trapped ions

Date and Time: Wednesday, March 31, 12:00 pm 

Location: Zoom 

Dissertation Committee Chair: Christopher Moroe

Committee: 

Norbert Linke
Alexey Gorshkov
Ronald Walsworth
Mohammad Hafezi 

Abstract: 

 We describe the inception, design, development, and initial results of The Cold Atom Vacuum Standard (CAVS). It has been known for many years that vacuum level limits the lifetime of a cold atom cloud, we invert this to create a vacuum pressure measurement tool based on the trapped cloud lifetime. The difference between a standard and a sensor is of great concern to metrologists: a primary standard defines a unit, and a sensor transduces it. To have a device capable of both functions is to have a calibration-free measurement tool, which is of interest to many stakeholders in academia, industry, and defense. We describe all aspects of construction of the CAVS, including a lengthy investigation of vacuum technology. We ultimately demonstrate that the device is traceable to pressure through the fundamental physics of collision cross sections, thereby elevating it to status as not just a sensor, but a standard

Dynamo is the mechanism that creates the magnetic fields of astronomical objects still, here conductive flows are organized is such way that the magnetic field self amplifies. We know that the Earth’s magnetic field has been changing in time, we even know that its magnetic field had a number of reversals, but we don’t have any predictive models for it. At the University of Maryland there is a model of the Earth’s core – The Three Meter Sodium spherical-Couette experiment that was designed to reproduce the geodynamo. While the first series of experimental runs were able to show that the apparatus can amplify an external magnetic field, there was no observable self-sustainable magnetic field. And on the top of that the experiment got damaged and needed to be repaired. Meanwhile numerical simulations done by Finke and Tilgner suggested that presence of a rough boundary between one surface of the experiment and the liquid sodium might allow us to reach the dynamos state. So, from here we designed and executed sodium transfer operations, upgraded the experiment, assembled it back and started new runs. At the same time, we developed a series of predictive codes using linear and nonlinear models, including Reservoir computers. These models were designed to forecast the time evolution of this high Reynolds number hegnetohydrodynamics experiment that are capable of predicting the behavior of the system. And in the long goal are planned to be used to learn and reproduce the dynamics of the geodynamo action. 

Chains of Josephson junctions are known to produce some of the largest kinetic per-unit-length inductance, which can exceed the conventional geometric one by about 10^4. However, the maximum total inductance is still limited by the stray capacitance of the chain, which results in parasitic self-resonances. This stray capacitance is unnecessarily large in most circuits due to the high dielectric constant of silicon or sapphire substrates used. Here, we explore a regime of ultra-high impedance superconducting circuits by introducing the technique of releasing the Josephson chain off the substrate. The ultra-high impedance regime, defined as an impedance which exceeds 4 times the resistance quantum (4Rq ~ 25.8 kOhms), is realized in this work by combining a maximal per-unit-length inductance with a minimal stray capacitance and demonstrates the highest impedance electromagnetic structures available today. We begin with suspended “telegraph" transmission lines, composed of 30,000+ junctions and show that the wave impedance can exceed 5 times Rq (33 kOhms) while the line still maintains a negligible DC resistance. To quantify the effects of parasitic chain modes in ultra-high impedance circuits, we use high-inductance fluxonium qubits. We show that chain modes are ultra-strongly coupled to the qubit but can be moved to higher frequency with the Josephson chain releasing technique. Finally, we create a superconducting quasicharge qubit (blochnium), dual of transmon, whose impedance reaches over 30 times Rq (200 kOhms) with no evidence of parasitic modes below 10 GHz. This qubit completes the periodic table of superconducting atoms and demonstrates the dual nature of a small Josephson junction in ultra-high impedance circuits, which we probe in a DC experiment in the final chapter.

Quantum many-body systems with long-range interactions—such as those that decay as a power-law in the distance between particles—are promising candidates for quantum information processors. Due to their high degree of connectivity, they are potentially capable of generating entanglement more quickly than systems limited to local interactions, which may lead to faster computational speeds. The questions of the nature of the speed-ups they can achieve—as well as how to program these long-range systems to achieve such speed-ups—are, therefore, of prime theoretical interest.

To understand the nature of the speed-ups achievable, it is natural to consider the dual question, which is what are the fundamental speed limits in quantum many-body systems? Given that most systems relevant to quantum computation operate in the non-relativistic regime—where information typically propagates at velocities far below the threshold set by the speed of light—the absence of an absolute speed limit seems to allow for unbounded rates of information transfer. However, in 1972, Lieb and Robinson restored a notion of locality in systems with local interactions by proving a bound that led to light-cone-like regions outside which information propagation is exponentially suppressed. The question of whether similar bounds could be proven for long-range systems has remained open—until recently.

In this thesis, we will describe results related to the now-fuller picture of the fundamental rates of information propagation in power-law-interacting systems. First, we consider the regime of ``strongly long-range'' interactions, for which velocities can grow unboundedly with system size. We will present Lieb-Robinson-type bounds for these systems and also outline a protocol that can transfer quantum states as fast as these bounds will allow. we will also discuss the implications of these bounds for quantum information scrambling.

The second part of the thesis will study how protocols for transferring quantum states quickly can be used to perform multi-qubit gates. In particular, we will demonstrate how the power of long-range interactions allows one to implement the unbounded fanout gate asymptotically faster than systems with local interactions. This result also implies the hardness of simulating the dynamics of long-range systems evolving for superlogarithmic times, and demonstrates the potential for insights from quantum many-body physics to lead to a more powerful toolbox for quantum computation.

Finally, we will address the question of fundamental speed limits in quantum systems that are open to the environment. A priori, it may seem surprising that such speed limits may exist, since non-unitary processes may break locality constraints. However, we show that under certain assumptions such as linearity and Markovianity of the bath, one can restore a notion of locality using Lieb-Robinson-type bounds. We use the resulting bounds to constrain the entanglement structure of the steady states of open long-range systems, a first step towards proving the area law for such systems.

Inference of the connectivity structure of a network from the observed dynamics of the states of its nodes is a key issue in science, with wide-ranging applications such as determination of the synapses in nervous systems, mapping of interactions between genes and proteins in biochemical networks, distinguishing ecological relationships between different species in their habitats etc. In this thesis, we show that machine learning models, trained for the forecasting of experimental and synthetic time-series data from complex systems, can automatically learn the causal networks underlying such complex systems. Based on this observation, we develop new machine learning techniques for inference of causal interaction network connectivity structures underlying large, networked, noisy, complex dynamical systems, solely from the time-series of their nodal states.

In particular, our approach is to first train a type of machine learning architecture, known as  the 'reservoir computer', to mimic the measured dynamics of an unknown network. We then use the trained reservoir computer system as an in silico model of the unknown network to estimate how small changes in nodal states propagate in time across that network. Since small perturbations of network nodal states are expected to spread along the links of the network, the estimated propagation of nodal state perturbations reveal the connections of the unknown network. 

We shall discuss how we can further apply this methodology to infer causal network structures underlying different time-series datasets and compare the inferred network with the ground truth whenever available. We shall demonstrate three practical applications of this network inference procedure in (1) inference of network link strengths from time-series data of coupled, noisy Lorenz oscillators, (2) inference of time-delayed feedback couplings in opto-electronic oscillator circuit networks designed the laboratory, and, (3) inference of the synaptic network from publicly-available calcium fluorescence time-series data of C. elegans neurons. In all examples, we shall also explain how experimental factors like noise level, sampling time, and measurement duration systematically affect causal inference from experimental data.

Given the general applicability of our machine learning methodology in time-series prediction and network inference, we anticipate that such techniques can be used for better model-building, forecast, and control of complex systems in nature and in the lab.

Parametric amplification of field modes is a prevalent phenomenon in pumped nonlinear systems. This mechanism is expected to interfere with the stability of low-energy states in periodically modulated Bose-Einstein condensates, which are described by a driven nonlinear equation. Motivated by the necessity to understand and mitigate dissipative mechanisms that curtail the applicability of Floquet engineering in bosonic optical lattices, the first part of this thesis outlines a framework that models the behavior of drive-induced instabilities in condensates subject to time-modulated lattice potentials. The predictions of this model are then contrasted with the results from an experimental investigation of the condensate depletion in shaken optical lattices, from which we assess the validity and limitations of our theory.
 
Ring-shaped energy bands, where a continuum of degenerate minima lie along a closed loop in momentum space, are of interest in ultracold fermionic and bosonic gases as the associated singularity in the density of states is expected to stabilize unconventional phases of matter. These moatlike dispersions are also linked to enhanced properties in solid-state materials. The second part of the thesis describes the realization of a Floquet-engineered Mexican-hat band using an amplitude modulated double-well optical lattice. Since our experimental approach allowed for the coherent preparation of condensed states in this hybridized Mexican-hat band, we also examined the stability of BEC states in the presence of this dispersion using the theoretical framework described in the first part of the thesis. Our observations are in fair agreement with the theoretical prediction that a BEC at the minimum of a moat dispersion lies at the edge of an instability region and should, hence, be unstable in any realistic scenario.

Floquet’s theorem says that any unitary, periodically driven system can be described by an effective time-independent Hamiltonian, where the effective Hamiltonian can have completely different properties than the static, undriven system.  Floquet engineering makes use of this idea to simulate new Hamiltonians that would otherwise not be possible in the undriven case.  For interacting systems, this approach can can be used to realize interesting correlated many-body states, but drive-induced heating must be understood and mitigated.  Cold atoms in optical lattices provide a controllable, well-isolated system in which these ideas can and have been realized. 

I describe research into two areas of Floquet engineering for interacting Bose-Einstein condensates in periodically driven optical lattices.  

The first half of this thesis focuses on the study of heating mechanisms for condensates in periodically driven lattices. In the weakly interacting limit, one might expect that heating could be described with a Fermi Golden Rule approach. Parametric driving of fluctuations in the condensate, however, can lead to runaway heating that cannot be described perturbatively.  We experimentally study heating in shaken 2D square lattices and demonstrate heating consistent with the theoretical predictions of parametric instabilities.

The second half of this thesis describes experiments that realize Floquet-induced effective staggered magnetic fields, and the relaxation dynamics of interacting particles subject to these fields. Interestingly, we observe pre-thermal relaxation dynamics, where an initially heated cloud suddenly subject to the effective Hamiltonian condenses into a state governed by the drive-induced effective Hamilton on a time scale faster than heating. 

Cryo-EM is an increasingly popular technique for determining the structure of solutions, especially of those with protein solutes. The ability to immobilize a fluid and attain atomic resolution of solutes within has propelled the technique to the forefront of electron microscopy.

Regular advancements in resolution, sample fabrication, and data collection and analysis means cryo-EM will continue to expand and find new and far reach applications.

In this thesis, a model system is proposed to address interface charging effects that are typically ignored when analyzing cryogenic electron microscope (EM) data. Cryo-EM sample fabrication rapidly solidifies through cooling the native fluidic state preventing short- and long-range ordering from occurring under slower cooling processes. The resulting vitreous state of the liquid is effectively a static representation of a liquid in a solid state. In this work, cryo-EM samples are fabricated with water, and then more complex solutions, to create a baseline understanding of the extent of surface charging from secondary electron emission. Subsequent solutions are investigated to expand the understanding of surface charging and study ion dispersion within the sample. The interferometry technique of off-axis electron holography is used to measure the relative electron-wave phase shift of the samples and is directly related to the electromagnetic fields native to the samples. The holography data is compared to finite-element simulations determining a surface charge of 1.5E-4C/m² is generated on each surface of the vitreous solution. The work is repeated with a solution of functionalized Au nanoparticles roughly 30nm in diameter suspended in DI water as a model system for more complex fluids. The mean inner potential of solution constituents is measured and compared to literature aiding in identifying the overall sensitivity of the technique and identifying necessary experimental improvements. 

With the rapid development of programmable quantum simulators, the quantum states can be controlled with unprecedented precision. Thus, it opens a new opportunity to explore the strongly correlated phase of matter with new quantum technology platforms. In quantum simulators, one can engineer interactions between the microscopic degrees of freedom and create exotic phases of matter that presumably are beyond the reach of natural materials. Moreover, quantum states can be directly measured instead of probing physical properties indirectly via optical and electrical responses of material as done in traditional condensed matter. Therefore, it is pressing to develop new approaches to efficiently prepare and characterize desired quantum states in the novel quantum technology platforms.

In this thesis, we discuss the preparation and characterization of the topologically ordered state in nobel quantum technological platforms. First, we show that optically driven monolayer graphene in the quantum Hall regime creates an effective bilayer quantum Hall system. It provides a flexible platform for engineering quantum Hall phases. We use infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED) to show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction 2/3. Moreover, at integer filling 1, the system exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions. 

Then we turn our attention to the characterization of the topological invariants from a ground state wave function of the topological order phase and the implementation in noisy intermediate quantum devices. Using topological field theory and tensor network simulations, we demonstrate how to extract the many-body Chern number (MBCN) given a bulk fractional quantum Hall wave function. We further propose an ancilla-free experimental scheme for measuring the MBCN without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function.

Finally, we discuss an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a ground state wave function of a gapped, translationally invariant Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We then use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully characterize topological order from the bulk of a ground state wave function.

Trapped atomic ions excel as local quantum information processing nodes, given their long qubit coherence times combined with high fidelity single-qubit and multi-qubit gate operations. Trapped ion systems also readily emit photons as flying qubits, making efforts towards construction of large-scale and long-distance trapped-ion-based quantum networks very appealing. Two-node trapped-ion quantum networks have demonstrated a desirable combination of high-rate and high-fidelity remote entanglement generation, but these networks have been limited to only a few meters in length. This limitation is primarily due to large fiber-optic propagation losses experienced by the ultraviolet and visible photons typically emitted by trapped ions. These wavelengths are also incompatible with existing telecommunications technology and infrastructure, as well as being incompatible with many other emerging quantum technologies designed for useful tasks such as single photon storage, measurement, and routing, limiting the scalability of ion-based networks.

In this thesis, I discuss a series of experiments where we introduce quantum frequency conversion to convert single photons at 493 nm, produced by and entangled with a single trapped ¹³⁸Ba⁺ ion, to near infrared wavelengths for reduced network transmission losses and improved quantum networking capabilities. This work is the first-ever to frequency convert Ba⁺ photons, being one of three nearly concurrent demonstrations of frequency converted photons from any trapped ion.  After discussing our experimental techniques and laboratory setup, I first showcase our quantum frequency converters that convert ion-produced single photons to both 780 nm and 1534 nm for improved quantum networking range, whilst preserving the photons' quantum properties. Following this, I present two hybrid quantum networking experiments where we interact converted ion-photons near 780 nm with neutral ⁸⁷Rb systems. In the initial experiment, we observe, for the first time, interactions between converted ion-photons and neutral Rb vapor via slow light. The following experiment is a multi-laboratory project where we observe Hong-Ou-Mandel interference between converted ion-photons and photons produced by an ensemble of neutral Rb atoms, where notably these sources are located in different buildings and are connected and synchronized via optical fiber. Finally, I describe an experiment in which we verify entanglement between a ¹³⁸Ba⁺ ion and converted photons near 780 nm. These results are critical steps towards producing remote entanglement between trapped ion and neutral atom quantum networking nodes. Motivated by these experimental results, I conclude by presenting a theoretical hybrid-networking architecture where neutral-atomic based nondestructive single photon measurement and storage can be integrated into a long-distance trapped-ion based quantum network to potentially improve remote entanglement rates.

The dynamo action is the process through which a magnetic field is amplified and sustained by electrically conductive flows. Galaxies, stars and planets, all exhibit magnetic field amplification by their conductive constituents. For the Earth in particular, the magnetic field is generated due to flows of conductive material in its outer core. At the University of Maryland, our Three-meter diameter spherical Couette experiment uses liquid sodium between concentric spheres to mimic some of these dynamics, giving insight into these natural phenomena. Numerical studies of Finke and Tilgner (Phys. Rev. E, 86:016310, 2012) suggest a reduction in the threshold for dynamo action when a rough inner sphere was modeled by increasing the poloidal flows with respect to the zonal flows and hence increasing helicity. The baffles change the nature of the boundary layer from a shear dominated to a pressure dominated one, having effects on the angular momentum injection. We present results on a hydrodynamics model of 40-cm diameter spherical Couette flow filled with water, where torque and velocimetry measurements were performed to test the effects of different baffle configurations. The selected design was then installed in the 3-m experiment. In order to do that, the biggest liquid sodium draining operation in the history of the lab was executed. Twelve tons of liquid sodium were safely drained in a 2 hours operation. With the experiment assembled back and fully operational, we performed magnetic field amplification measurements as a function of the different experimental parameters including Reynolds and Rossby numbers. Thanks to recent studies in the hydrodynamic scale model, we can bring a better insight into these results. Torque limitations in the inner motor allowed us to inject only 4 times the available power; however, amplifications of more than 2 times the internal and external magnetic fields with respect to the no-baffle case was registered. These results, together with time-dependent analysis, suggest that a dynamo action is closer than before; showing the effect of the new baffles design in generating more efficient flows for magnetic field amplification. We are optimistic about new short-term measurement in new locations of the parameter space, and about the rich variety of unexplored dynamics that this novel experiment has the potential to reach. These setups constitute the first experimental explorations, in both hydrodynamics and magnetohydrodynamics, of rough boundary spherical Couette flows as laboratory candidates for successful Earth-like dynamo action.

Gravitational-wave (GW) signals from the coalescence of almost a hundred binary black holes and neutron stars have been detected over the past few years. These observations have improved our understanding of compact binary systems, their properties, and astrophysical formation channels. GWs also probe gravity in the nonlinear, strong-field regime, thus allowing us to search for, or constrain, deviations from general relativity.

The focus of this dissertation is improving the analytical description of binary dynamics, which is important for producing accurate waveform models that can be used in searching for GW signals, inferring their parameters, and testing gravity. The research presented here can be divided into three complementary parts: 1) extending the post-Newtonian (PN) approximation for spinning binaries to higher orders, 2) improving effective-one-body (EOB) waveform models, and 3) identifying some signatures of modified gravity theories in waveforms.

The PN approximation, valid for slow motion and weak gravitational field, is widely used to model the dynamics of comparable-mass binaries, which are the main GW sources for ground-based detectors. We derive PN results for spinning binaries at the third- and fourth-subleading PN orders for the spin-orbit coupling, and at the third-subleading order for the spin(1)-spin(2) coupling. We adopt an approach that combines several analytical approximation methods to obtain PN results valid for arbitrary mass ratios from gravitational self-force results at first order in the mass ratio. This is possible due to the simple mass dependence of the scattering angle in the post-Minkowskian approximation (weak field but arbitrary velocities).

The EOB formalism produces accurate waveforms by combining analytical results for the binary dynamics with numerical relativity information, while recovering the strong-field test-body limit. To improve EOB models, we include spin-precession effects in the Hamiltonian up to the fourth PN order, and extend the radiation-reaction force and waveform modes to eccentric orbits. We also assess the accuracy of post-Minkowskian results, for both bound and scattering orbits, and incorporate them in EOB Hamiltonians.

In the context of modified gravity theories, we derive the conservative and dissipative dynamics in Einstein-Maxwell-dilaton theory at the next-to-leading PN order, and compute the Fourier-domain gravitational waveform. We also develop a theory-agnostic effective-field-theory approach for describing spontaneous and dynamical scalarization: non-perturbative phenomena in which compact objects can undergo a phase transition and acquire scalar charge. We apply this approach to binary black holes in Einstein-Maxwell-scalar theory using a quasi-stationary approximation, then extend it to account for the dynamical evolution of the scalar charge, and apply it to binary neutron stars in a class of scalar-tensor theories.

Improving waveform models is important for current-generation GW detectors and necessary for future detectors, such as LISA, the Einstein telescope, and Cosmic Explorer. The results obtained in this work are important steps towards that goal.

The study of quantum information provides a common lens to our investigation of quantum mechanical phenomena in various fields, including condensed matter, high energy, and gravitational physics. This thesis is a collection of theoretical and numerical studies of the dynamics of quantum information in quantum many-body systems, focused on characterizing the scrambling of information and entanglement dynamics in generic dynamical setups.

In the first part of the thesis I study out-of-time-ordered correlators (OTOCs) as a probe for quantum information scrambling. By computing OTOCs in disordered quantum spin systems we find that disorder leads to distinct patterns of scrambling, and can arrest the information propagation significantly for high enough values of disorder. I also study the generic features of finite temperature OTOCs in gapped local systems and their relation to the temperature bound on chaos, using a combination of numerical and analytical approaches.

In the second part of the thesis, I study analytically tractable models of measurement-induced entanglement transition. Frequent measurements in a quantum circuit lead to distinct entanglement phases of the prepared quantum state. Using these models, we find effective field theories describing the entanglement patterns and the entanglement phase transitions. By considering generalizations of these models, we find that long-range interactions in the quantum circuit lead to novel entanglement phases with efficient emergent error-correcting properties.

In the last part of the thesis, I study tensor network states defined on generic sparse graphs. Using the intuition that generic graphs are locally tree-like, I develop efficient numerical methods to access local information of such states, which serve as a pathway for studying quantum many-body physics on sparse graphs beyond lattices.

In this thesis, we present the construction of a new apparatus for conducting experiments with ultracold strontium. The new apparatus is designed with a high-flux atomic source, a custom science chamber optimized for optical access, high-current Bitter electromagnets, and an updated computer control system. We discuss in-depth the implementation of an insulated-gate bipolar transistor (IGBT) for fast current control of the magnetic field coils. We also present the design of JQI AutomatioN for Experiments (JANE): a programmable system on chip (PSoC)-based pseudoclock device that we use as the main clocking device for our experiments.

Next, we report the realization of the first magneto-optical trap (MOT) of an alkaline-earth atom with a tetrahedral trap geometry produced by a nanofabricated diffraction grating. We have demonstrated a broad-line MOT in bosonic ⁸⁸Sr and fermionic ⁸⁷Sr. We trap approximately 4x10⁷ atoms of ⁸⁸Sr and achieve temperatures of around 6 mK, with a trap lifetime of around 1 s.

Finally, we demonstrate sawtooth wave adiabatic passage (SWAP) in a narrow-line MOT of ⁸⁸Sr atoms. In the narrow-line MOT, we trap approximately 3x10⁶ atoms, with an average temperature of 3.4 µK and a trap lifetime of 0.77 s. We also discuss the possibility for a narrow-line grating MOT of the fermionic isotope. Our work with strontium grating MOTs is a step in the direction of compact quantum devices with alkaline-earth atoms.

As the demand for internet access rose over the past two decades, the information-carrying capacity of standard single mode fibers has grown in tandem, as information was multiplexed over the many degrees of freedom of light: wavelength, polarization, phase, amplitude and time. We are soon, however, approaching the theoretical information-carrying capacity limit of SMFs. This has spurred significant research interest in understanding wave propagation in multimode optical fibers (MMFs), where an additional spatial degree of freedom is present.

Similar to SMF systems, nonlinear propagation effects are expected to play an important role in determining the capacity and performance of MMF-based systems. Over the past decade, numerous complex spatiotemporal nonlinear optical effects have been experimentally observed in MMFs, such as Kerr-induced beam self-cleaning, parametric instability processes, multimode solitons and ultrabroadband supercontinuum generation. This has sparked an interest in understanding multimode nonlinearity from a fundamental and applied physics perspective.

Experimental characterization of intermodal nonlinear effects between individual fiber modes is of central importance in developing a full understanding of nonlinear propagation physics in MMFs. However, this has remained relatively under-studied as most literature reported thus far focuses on complex phenomena in the presence of hundreds of co-propagating spatial modes. Additionally, experimental characterization methods used thus far have been limited to conventional imaging, time- and spectral-domain methods that average over either the spatial or temporal dimensions, and are therefore not capable of fully resolving the spatiotemporal phenomena.

In this defense talk, I describe our work on developing new methods to selectively excite a small number of fiber modes and spatiotemporally characterize nonlinear interactions between them in three different fiber systems: step-index few-mode fibers (FMFs), parabolic-index MMFs, and hollow ring-core fibers (RCFs) that support stable propagation of modes that carry well-defined orbital angular momentum (OAM). First, I discuss our observation of a novel nonlinear mode interference effect in a step-index FMF where two modes were selectively excited. Second, I describe our spatiotemporal measurements of the previously-observed Kerr-induced beam self-cleaning phenomenon. And finally, I report our work on OAM fiber modes, where we recently discovered a spatially-generalized version of the nonlinear polarization rotation effect known from SMF nonlinear optics.

This thesis describes the construction of a new laboratory and a new apparatus for ultracold strontium experiments. It also describes the creation of the first strontium grating magneto-optical trap (MOT). The new strontium apparatus has been improved to provide high, and controllable atomic flux, high magnetic field coils, low vacuum pressure, plenty of optical access, and a streamlined computer control system. This flexible apparatus is designed to operate several potential experiments.

Our work with strontium grating MOTs will help to enable the creation of compact, stable, and portable quantum devices that harness the unique capabilities of alkaline earth atoms. We present the construction of the grating MOT apparatus, the demonstration of the broad line strontium grating MOT, and the transfer to the narrow line grating MOT. In addition, we show the effectiveness of sawtooth wave adiabatic passage (SWAP) in the grating MOT geometry.    

Lastly, we present work from the previous apparatus, measuring the isotope shifts on the clock and intercombination transitions in strontium.

We report recent achievements toward understanding the nanoscale two-level systems (TLS) within the oxide layers of aluminum. TLSs create a major decoherence source in quantum information processors. We utilize three techniques to understand TLS, i.e., (1) a traditional power dependent loss, which provides the information of collective TLS effects, (2) spectroscopy of individual TLSs by DC-tuning and (3) two-tone spectroscopy of ensemble TLSs by a second saturation tone. We realize the behaviors of TLSs in different structural phases have distinguished features. Utilizing the DC-tuning feature of our sensor, we further extract dipole moments from individual TLSs and provide the moment histograms of two aluminum oxide films. We observe polycrystalline oxide has small average dipole moment and a single-peak histogram suggesting a single TLS origin. On the other hand, amorphous oxide has a wide spread of dipole moment values probably due to the nature of oxygen deficiency content. TLSs in both bulk films show a square root dependency of power indicating the TLSs can be treated as stable in frequency. However, TLSs on the surface fit well with the model assuming that TLS frequencies are under stochastic fluctuations resulting in a weak dependency of power. Moreover, TLSs in polycrystalline phase are relatively stable in the time domain than TLSs in amorphous phase. 

This thesis is the result of work on two separate Bose-Einstein condensate (BEC) experiments. First, I describe several projects in the construction of an ultracold Er and Na mixture experiment (Er:Na experiment). These include the design and characterization of a high temperature induction oven for Er as well as the capture of Er atoms into a 2D magneto-optical trap (2D MOT). Together, the induction oven and 2D MOT constitute a novel, compact source of cold Er atoms. Additionally, the construction and characterization of high current magnetic field coils for a magnetic quadrupole trap (MQT) and Helmholtz coils for future Feshbach spectroscopy are detailed.

Second, I describe a series of experiments with spinor gases carried out on the JQI Na spinor apparatus. In the first experiment, I demonstrate the freezing of nonlinear spin mixing dynamics in a 23Na BEC using a microwave dressing. This technique can be used to preserve squeezing of a probe state in future metrological applications. The spinor phase of a frozen state evolves at an enhanced rate proportional an effective quadratic Zeeman shift, q, of the |F = 1, mF = 0⟩ energy level.

In the second experiment, I demonstrate a radio frequency (rf) atomic spin-1 Ramsey interferometer which can measure the effective q, and thereby the spinor phase precession rate of a frozen probe state. The interferometer can simultaneously measure the rf detuning and q, and I demonstrate that it can be operated in both resonant and off-resonant regimes, using differential phase modulation between the two Ramsey pulses. The spin-1 Ramsey interferometer therefore has distinct advan- tages over both rf and microwave Rabi spectroscopy which are alternative methods to measure the effective q.

Finally, I demonstrate theoretical grounds for spin squeezing in a cold spin-1 thermal gas. In particular, I derive a spin-1 Boltzmann transport equation for the Wigner phase space density operator without recourse to Hartree-Fock theory. I then apply three different theoretical paradigms to model an experimental observation of classical relative number squeezing in a cold spin-1 thermal gas of Na: a simplified undepleted pump model which I solved analytically, a semiclassical quasiprobability distribution (QPD) numerical method, and numerical solution of the Schro ̈dinger equation using Fock states.

The nature of dark matter is a crucial problem for both cosmology and particle physics. The weakly interactive massive particle (WIMP) is one of the top dark matter candidates searched for decades because of the so-called ‘WIMP-miracle’. Dual phase liquid xenon time projection chambers (LXeTPC) have led the most sensitive searches on the GeV-scale spin-independent WIMP-nucleus scattering cross section for years because of the strong background suppression and scalability. With 3.7 tonne liquid xenon in the sensitive region of the LXeTPC, the Particle AND Astrophysical Xenon (PandaX) collaboration is now running PandaX-4T experiment at the B2 Hall of China Jinping Underground Laboratory after the PandaX-II experiment. The strongest limit back to the release time was published with the 0.63 tonne·year exposure on the standard thermal WIMP search with a lowest excluded cross section (90% C.L.) of 3.8 × 10^(−47) cm^2 at a dark matter mass of 40 GeV/c^2.

In this dissertation, I discuss research and developments correlated to PandaX experiments. I present the whole procedure of Rb-83/Kr-83m calibration in the PandaX-II detector from sources production with 3.4/20 MeV protons bombardment on natural krypton to the data analysis after injection into the PandaX-II detector, which becomes crucial for the increasingly larger detectors. With the Kr-83m events, the horizontal position construction algorithms in PandaX-II are improved, which is important to fully take advantage of the self-shielding ability of xenon, determining the fiducial volume directly related to the exposure. Moreover, I discuss the procedure of the profile likelihood ratio analysis to set the limits and sensitivities, where probability distribution functions are prepared with reweighting Monte Carlo to handle the systematic uncertainties in the detector response modeling more robustly. The methodology is applied on the spin-independent WIMP search to prove consistency with the template morphing method. Then, I conduct a search on electronic absorption of sub-MeV fermionic dark matter which shares similarities with sterile neutrino dark matter. Such dark matter with a 60 keV/c^2 mass can explain the low-energy ER excess reported by XENON1T collaboration, but is only marginally allowed by our constraints.

This dissertation presents experimental research into the nonlinear propagation of Terawatt class lasers in air over 1—40 m. Lasers of this power undergo filamentation; Kerr lensing in air leads to self-focusing which is arrested by photoionization. For λ = 800 nm the dynamic balance of self-focusing and plasma defocusing generates beams with a ~100 µm transverse size that is maintained over many meters. Heating from plasma recombination and relaxation of molecular rotations generates a single cycle acoustic wave and thermal profile which dissipates on the millisecond timescale.

We first use a novel array of synchronized microphones to observe extended air heating from a single laser shot. Single shot measurements allow the observation of air turbulence effects highlighting their importance even in a controlled lab environment. Armed with new knowledge about air heating we demonstrate filament applications for fog clearing, triggering high voltage spark gaps, and generating air waveguides. We show that both fog clearing and high voltage spark gap triggering are possible with air heating driven primarily by resonantly excited rotational states of air molecules rather than plasma. By utilizing beam shaping and multi-filamentation we demonstrate long range air waveguides limited only by the 40 m length of our test range.

Majorana zero modes (MZMs) can be fault-tolerant topological qubits due to their topological protection property and non-Abelian statistics. Over the last two decades, a deluge of theoretical predictions and experimental observations has been actively ongoing in the hope of implementing topological quantum computation upon MZMs. Among several solid-state systems, the most promising platform to realize MZMs is the one-dimensional semiconductor-superconductor nanowire (called ``Majorana nanowire'' in short), which is the focused system in this thesis. It is fundamental to identify MZMs as qubits to construct topological quantum computers. Therefore, the signatures of MZMs become highly crucial for verification. However, the earlier theoretical works demonstrate that topologically trivial Andreev bound states (ABSs) can mimic the hallmarks of MZMs in various aspects but do not carry topological properties. As a result, distinguishing MZMs from ABSs becomes significantly pivotal in the study of Majorana nanowire.

One of the signatures the author studied is the robustness of the quantized zero-bias conductance peak (ZBCP) in the realistic Majorana nanowire. The importance of this signature becomes further enhanced, particularly after the 2018 Nature paper, which displayed the quantized Majorana conductance, got retracted. In Chapter 2, the proposed quality factors quantify the robustness of quantized ZBCPs. By comparing the numerical results between different scenarios, this study shows that the quality factor $F$ can help distinguish topological MZMs from trivial subgap bound states in the low-temperature limit.

Another necessary signature of MZMs is the non-local correlation. In Chapter 3, the conductance correlation is demonstrated by modeling the comparing quantum-point-contact (QPC) conductance from each end. Both the pristine nanowire and the quantum-dot-hybrid-nanowire system are modeled and compared, which shows the significance of non-local end-to-end correlation for the existence of MZMs. The other approach to simultaneously examining the localization of states at both ends of the nanowire is through the Coulomb blockade (CB) measurement. The lack of sensitivity to the localized state at only one end makes the CB spectroscopy able to capture the non-local correlation feature of MZMs. However, CB transport in the Majorana nanowire is much more complicated to analyze than QPC transport because (a) Coulomb interaction is treated as equal to MZM physics without perturbation, and (b) there are many energy levels in the nanowire, which gives rise to an exponential complexity to solve the rate equations. In Chapter 4, a generalized version of Meir-Wingreen formula for the tunneling conductance of a two-terminal system is derived. This formula reduces the exponential complexity of the rate equations to as low as the linear complexity of QPC tunneling, thus allowing multiple energy levels to be included in the calculation. With dominant realistic effects in the model, the experimental features, such as the bright-dark-bright CB conductance pattern and decreasing oscillation conductance peak spacings (OCPSs) with the Zeeman field, will be simulated and explained theoretically.

In short, the theoretical methods proposed in this thesis, including the quality factors, non-local correlation ZBCPs, and CB spectroscopy, are intended to distinguish MZMs from other topologically trivial bound states. Further investigations on the robustness of quantized conductance and non-local correlation analysis can clarify the ambiguous signals in the experiments and push the realization of topological quantum computation to the frontier.

In this dissertation, we discuss the applications of intense mid-infrared laser interactions in three main topics. First, we demonstrate and discuss the remote detection of radioactive materials using avalanche breakdowns driven by picosecond, mid-infrared laser pulses. In the presence of radioactive materials, an enhanced population of free electrons and weakly bound ions are created in air. Laser driven avalanche ionization is a powerful tool for amplifying and detecting this weak signature, allowing for detection at standoff distances beyond the stopping distance of the radioactive particles. This technique can be applied more generally to the detection of any low density plasma. In the second section, we apply a similar method to measure laser ionization yields in atmospheric pressure gas across an extremely wide range. Finally, we demonstrate and discuss the generation of THz and low harmonics from two-color mid-infrared laser pulses. This technique allows for the generation of highly efficient, ultra-broadband coherent radiation.

Majorana zero modes are neutral zero-energy localized excitations emerging in the low-dimensional condensed matter systems, which are their own antiparticles. These excitations are topological with an intrinsic ground-state degeneracy, belonging to the (SU­₂­)₂ algebra and obeying the non-Abelian anyonic braiding statistics, which provides a possibility to implement the fault-tolerant topological quantum computing. As a result, enormous experimental efforts have focused on the realization of the Majorana zero modes, especially in the one-dimensional superconductor-semiconductor Majorana nanowires during the past decade. Although experiments have observed the zero-bias conductance peaks, these experimentally observed peaks are not robustly quantized as theoretically predicted for the signature of Majorana zero modes, and many other hallmarks of Majorana zero modes are yet to be unambiguously confirmed in experiments, which makes the experimentally observed zero-bias conductance peaks being interpreted as the Majorana zero modes questionable.

Therefore, in this dissertation, we carry out a detailed theoretical analysis of the experimental results, and classify the experimentally observed zero-bias conductance peaks into three types: the good (i.e., the actual topological Majorana zero modes), the bad (i.e., which is the partially-separated quasi-Majorana modes induced by the inhomogeneous potential and quantum dot in the nanowire), and the ugly (i.e., which is the trivial low energy fermionic state induced by random disorder). Our study concludes that almost all the current experimentally observed zero-bias conductance peaks in the publications are the ugly zero-bias conductance peaks, and future experiments should focus on the improvement of the material quality to reduce disorder.

Cold atoms trapped in optical lattices have been proven to be a versatile, well-controlled and powerful platform for simulating and studying physics, from condensed matter systems to high energy physics and cosmology. However, the diffraction limit restricts the spatial resolution of light-induced confinement and measurement. Since the length scale of confinement sets a characteristic energy scale of the system, it is desirable to circumvent this diffraction limit to provide more control of the associated energy scale.

In the first half of this thesis, I describe a series of experiments that exploit the nonlinear optical response in the three-level system of 171Yb to realize subwavelength spatial control and measurement of cold atoms. First, I report the experimental realization of a conservative optical lattice for cold atoms with subwavelength spatial structure. The three-level system is coupled by two laser fields in a way that the dark state of the three-level system changes its spin composition over a narrow spatial region. The kinetic energy associated with this large gradient in the spin composition creates a lattice of narrow barriers with a width of 10 nm, which is one-fiftieth of the laser wavelength. Extending from this, I describe the realization of a wave-function density microscope with a spatial resolution of 10 nm and temporal resolution of 500 microseconds. Using the sharp spatial dependence in the spin composition of the dark state, we shelve narrow slices of the wavefunction within every unit cell of the lattice into selected spin state, which is then selectively read out to achieve subwavelength measurement of the atomic probability density. Finally, I report the stroboscopic realization of a λ/4-spaced lattice. We stroboscopically apply shifted versions of the lattice of narrow barriers mentioned earlier, thereby creating an effective time-averaged potential with a lattice spacing of λ/4.

In the past decade, significant progress has been made by extending the control of atoms to the single atom level, and single neutral atoms optically trapped in arrays have emerged as a compelling and scalable platform for quantum simulation and computing. A natural step is to extend to multi-species systems, which will help solve challenges encountered in single-species platforms.

In the second half of the thesis, I motivate and describe the construction of a new dual-species tweezer array apparatus. An inherent challenge in single-species platforms is the crosstalk between atoms due to the scattered photons from nearby atoms during site-selective control and measurement. A dual-species architecture with Rb and Yb can suppress unwanted crosstalk and even allow parallel tasking on Rb and Yb separately due to the large separation in resonance frequencies. Moreover, the use of multi-species atoms provides an extra tuning knob that is useful in realizing multi-qubit gates. By manipulating the substantial difference in the intra- and inter-species van der Waals force, multi-qubit gates could be realized on Rb and Yb, giving significant speedups for some quantum algorithms and error-correction schemes.

This thesis deals with the rigorous analysis of two models of superfluidity. One of them is a macro-scale description of the interacting dynamics of a mixture of superfluid Helium and normal Helium. The equations used are modifications of the incompressible Navier-Stokes equations in 2D, with a nonlinear mutual friction that couples the two fluids. We show global well-posedness of strong solutions (with high-regularity data) to this model, by proving a Beale-Kato-Majda-type condition.

Next, we study a micro-scale model (the “Pitaevskii’’ model) of superfluid-normal fluid interactions, derived by Lev Pitaevskii in 1959. This involves the nonlinear Schrödinger equation and incompressible inhomogeneous Navier-Stokes equations. Mass and momentum exchange between the two fluids is mediated through a nonlinear and bidirectional coupling. We establish the existence of local solutions (strong in wavefunction and velocity, weak in density) that satisfy an energy equality.

Finally, we prove a weak-strong type uniqueness theorem for the solutions of the Pitaevskii model.  We begin by arguing that for weak solutions whose regularity is governed purely by the energy balance equation, it is not possible to prove weak-strong uniqueness, even if the strong solution is as smooth as one wishes. Thus, we are forced to consider slightly less weak solutions obtained from a higher-order energy bound. Owing to their better regularity, we can compare them to moderate solutions – which are rougher than conventional strong solutions used for this purpose – and establish a weak-moderate uniqueness theorem. Relative to the solutions actually constructed in the earlier part of this thesis, only some of the regularity properties are used, allowing room for improved existence theorems in the future, while maintaining compatible uniqueness results.

Quantum systems are prone to noises. Accordingly, many techniques are developed to cancel the action of a quantum operation, or to protect the quantum information against the noises. In this dissertation, I discuss two such schemes, namely the recovery channel and the quantum error correction, and various scenarios in which they are applied.

The first scenario is the perfect recovery in the Gaussian fermionic systems. When the relative entropy between two states remains unchanged under a channel, the perfect recovery can be achieved. It is realized by the Petz recovery map. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel.

The second scenario is the approximate recovery in the context of quantum field theory. When perfect recovery is not achievable, the existence of a universal approximate recovery channel is proven. The approximation is in the sense that the fidelity between the recovered state and the original state is lower bounded by the change of the relative entropy under the quantum channel. This result is a generalization of previous results that applied to type-I von Neumann algebras. To deal with quantum field theory, the type of the von Neumann algebras is not restrained here. This induces qualitatively new features and requires extra proving techniques. This results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms.

The third scenario is applying quantum error correction codes on tensor networks on hyperbolic planes. This kind of model is proposed to be toy models of the AdS/CFT duality, thus also dubbed holographic tensor networks. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility, we provide guidelines for constructing networks consisting of multiple types of tensors which are efficiently contractible variational ansatzes, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. An explicit construction of such networks is also provided. It approximates the holographic HaPPY pentagon code when variational parameters are taken to be small.

Topological quantum error-correcting codes are a family of stabilizer codes that are built using a lattice of qubits. The stabilizers of the code are local, and logical information is encoded in the non-local degrees of freedom. From the condensed matter perspective, their code space corresponds to the ground state subspace of a local Hamiltonian belonging to a non-trivial topological phase of matter. Conversely, one can use fixed point Hamiltonian of a topological phase to define a topological quantum error-correcting code.

This close connection has motivated numerous studies which utilize insights from one viewpoint to address questions in the other. This thesis further explores the possibilities in this direction. In the first two parts, we present novel schemes to implement logical gates, which are motivated by the condensed matter perspective. In the third part, we show how the quantum error correction perspective could be used to realize robust topological entanglement phases in monitored random quantum circuits. And lastly, we explore the possibility of extending this connection beyond topological quantum error-correcting codes. In particular, we introduce an order parameter for detecting k-local non-trivial states, which can be thought of as a generalization of topological states that includes codewords of any quantum error-correcting code.

Analyzing time series from complex dynamical systems in nature is a common yet challenging task in scientific computation since these time series are usually high-dimensional. To apply our physics intuitions to these dynamical systems often requires projecting these time series to certain low-dimensional degrees of freedom, which often introduces complicated memory effect. In this work, we examine such memory effect within time series generated from Langevin dynamics, Molecular Dynamics (MD) and Monte Carlo (MC) simulations, and some experimental time series. We also develop computational methods to minimize and model such memory effects using statistical mechanics and machine learning.

In recent years, MD simulation has become a powerful tool to model complex molecular dynamics in physics, chemistry, material science, biology, and many other fields. However, rare events such as droplet formation, nucleation, and protein conformational changes are hard to sample using MD simulations since they happen on the timescales far away from what all-atom MD simulation can reach. This makes MD simulation less useful for studying the mechanism of rare event kinetics. Therefore, it is a common practice to perform enhanced sampling techniques to help sample rare events, which requires performing dimensionality reduction from atomic coordinates to a low-dimensional representation that has a minimal memory effect.

In the first part of this study, we focus on reducing the memory effect by capturing slow degrees of freedom using a set of low-dimensional reaction coordinates (RCs). These RCs can then be used to help reproducing correct kinetic connectivity between metastable states using enhanced sampling methods such as metadynamics. We demonstrate the utility of our method by applying them to the droplet formation from the gaseous phase of Lennard-Jones particles and the conformational changes of a small peptide Ace-Ala$_3$-Nme.

The second part of the study aims at modeling another type of memory coming from intrinsic long-term dependency induced by ignored fast degrees of freedom wherein we utilize one of the fundamental machine learning techniques called the recurrent neural network to model non-Markovianity within time-series generated from MD simulations. This method has been shown to work not only on the molecular model of alanine dipeptide but also on experimental time series taken from single-molecule force spectroscopy. At the end of this second part, we also improve this method to extrapolate physics that the neural network had never seen in the training dataset by incorporating static or dynamical constraints on the path ensemble it generates.

In this thesis we describe a novel regime of cavity quantum electrodynamics, where a single atom is coupled to a multi-mode Fabry-Perot cavity with a strength much larger than its free spectral range. In this regime, the atom acting as a quantum impurity mediates interactions between many-body states of radiation in the multi-mode cavity. This novel regime of cavity QED is experimentally realized by coupling superconducting artificial atoms to a high impedance 1-D superconducting transmission line cavity. We study the problem of single photon decay in these strongly non-linear cavities with discrete energy levels. By engineering the properties of the artificial atoms, we alter interaction and connectivity between many-body states of radiation, and we observe two distinct effects. For the case of a multi-mode Fabry-Perot cavity coupled to a fluxonium artificial atom, the interactions mediated by the atom attempts to split a single photon into two low frequency photons but fails because of limited connectivity in the many-body Fock space. This phenomenon of many-body localization of radiation gives rise to striking spectral features where a single standing wave resonance of the cavity is replaced by a fine structure of satellite peaks. On the other hand, for the case of a transmon coupled galvanically to the cavity, the interaction splits a single photon at high energy into a shower of odd number of lower energy photons. In this case the single standing wave resonance of the cavity acquires a shorter lifetime which can be calculated using Fermi's golden rule and matches our theoretical model without any adjustable parameters.

This dissertation explores quantum computing applications of fluxonium superconducting circuits. Fluxonium's high coherence time T₂ and anharmonicity make it an excellent platform for both digital quantum processors and analog quantum simulators. Focusing on the digital quantum computing applications, we report recent work on improving the T₂ and gate error rates of fluxonium qubits. Through enhancements in fabrication methods and engineering of fluxonium's spectrum, a coherence time in excess of 1 millisecond is achieved, setting a new standard for the most coherent superconducting qubit. This highly coherent device is used to demonstrate a single-qubit gate fidelity greater than 99.99%, a level of control that had not been observed until now in a solid-state quantum system. Utilizing the high energy relaxation time T₁ of the qubit transition, a novel measurement of the circuit's parity-protected 0-2 transition relaxation time is performed to extract additional sources of energy loss.

To demonstrate fluxonium's utility as a building block for analog quantum simulators, we investigate how to simulate quantum dynamics in the Transverse-Field Ising Model (TFIM) by inductively coupling 10 fluxonium circuits together. When the fluxonium loops are biased at half integer values of the magnetic flux quantum, the spectrum is highly anharmonic, and the qubit transition is well-approximated by a spin-1/2. This results in an effective Hamiltonian that is equivalent to the TFIM. By tuning the inter-qubit coupling across multiple devices, we can explore different regimes of the TFIM, establishing fluxonium as a prominent candidate for use in near-term quantum many-body simulations. 

Cells can sense and adapt motility to various external cues, such as chemoattractant, dc electric fields (EFs), and the physical properties of surroundings. This ability is essential to maintain normal physiological processes, and the malfunction may lead to severe diseases, such as cancer and autoimmune disease. Recent studies have observed waves of colocalized actin, associated with its upstream signaling molecules, drive cell directional migration. Furthermore, a coupled signal transduction excitable system – cytoskeleton excitable system (STEN-CEN) was revealed to regulate wave formation in the non-neural cell types. The system display hallmarks of excitability, such as refractory periods, all-or-none type response, and wave behaviors. Changing the states of STEN-CEN leads to the transition of migrational modes, which are typically observed across cell types.

This dissertation uses molecular experiments, computer vision quantification techniques, and modeling to understand how cells sense different external cues. Numerous studies have shown that there exist multiple parallel signal pathways sensing certain external stimuli, which suggests that the external signal is not sensed by a single molecule. Here I investigate the possibility of the STEN-CEN wave as the sensing unit to external cues. To overcome the challenge that wave dynamics are coupled with cell motion in normal-sized cells, I electro-fuse tens of Dictyostelium discoideum (D. d) cells together to giant cells. In giant cells, waves are no longer localized at the cell perimeter. The larger basal membrane area provides the opportunity to study the subcellular dynamics. I record the dynamics of F-actin and phosphatidylinositol (3,4,5)-triphosphate (PIP3), which represent CEN and STEN, respectively. To further decouple STEN and CEN, I apply a variety of chemical perturbations to suppress/activate STEN and CEN separately. Because the wave properties characterize the stage of STEN-CEN, I develop a series of quantification tools to measure wave area, duration, and speed. I collaborate with theorists to create a reaction-diffusion system model that recreates the experimental results.

The dissertation focuses on studying the role of STEN-CEN waves in sensing nanotopography and dc EF. CEN is found to directly sense the nanotopographical cue, forming long-lasting F-actin puncta at ridges in the absence of STEN. At the same time, STEN is essential for long-range wave behaviors for macro-domain nanoridges sensing. STEN and CEN cooperate in the sensing of the EF signals. According to the quantitative studies of wave properties, nanotopography changes the dimensionality and lifetime of waves, while EF can alter the activation thresholds of the intracellular systems. In summary, this thesis shows that the excitable biomechanical and biochemical wave system act as the sensing unit to the physical properties of the extracellular environment. As a result, cells can dynamically sense their surroundings and coordinate intracellular processes to migrate under the external cue guidance.

In this thesis, we present a theoretical study of energy absorption in chaotic systems subject to a rapid, time-periodic external drive. Periodic driving can facilitate a rich range of classical and quantum dynamical behaviors, including synchronization, dynamical stabilization, and chaos. Recent theoretical and experimental work has aimed to identify nonequilibrium “phases of matter” that might emerge in periodically driven systems, including prethermal states and discrete time crystals. However, energy absorption poses a potential obstacle to stabilization of these nonequilibrium states, particularly in quantum systems, where the persistence of the system’s quantum properties may be contingent on careful isolation of the system from its environment. For these systems, energy gain from the drive cannot be balanced by dissipation into a thermal bath, and so the only way to maintain a steady state is to suppress energy absorption entirely. As a result, much work has been devoted to understanding energy absorption, and the conditions under which it might be suppressed, in periodically driven, thermally isolated classical and quantum systems.

Motivated by these general concerns, we narrow our focus towards model systems with chaotic, ergodic dynamics; such models are the cornerstone of the modern understanding of statistical mechanics and thermalization. Specifically, we begin our analysis with classical periodically driven chaotic systems, in the high-frequency driving regime. In this limit, we find that energy absorption in these systems is described by a process of diffusion in energy space. This energy diffusion model predicts a three-stage process of energy evolution: Initial relaxation to a prethermal state, followed by slow evolution of the system’s energy probability distribution in accordance with a Fokker-Planck equation, followed by either unbounded energy absorption or relaxation to an infinite temperature state. The rate of energy absorption predicted by this model is found to be consistent with a range of theoretical and numerical studies of both classical and quantum systems, which have found heating rates which are exponentially or quasi-exponentially small in the frequency of the drive.

After investigating the general features of the energy diffusion description, we then explore this framework as it applies to different classes of systems. First, we look at energy absorption in dynamical billiard models, in which a particle in a cavity is subjected to a rapid periodic driving force. For these systems, we obtain simple, explicit expressions for the rates of energy absorption and diffusion, and we find good agreement between these results and numerical simulations. Moreover, we find that this analysis for billiard models may be generalized to many-particle billiard systems, offering a window into how energy absorption can occur in many-body interacting systems. We then apply the energy diffusion description to one-dimensional oscillator systems, driven by weak noise. For these systems, the Fokker-Planck equation describing energy diffusion is especially simple and can be solved exactly in some cases. Finally, we look to periodically driven quantum chaotic systems, and begin to probe whether such systems may be described by the classical energy diffusion model. We discuss the theoretical tools necessary to understand this possible connection, including Floquet theory and random matrix theory. We conclude with a heuristic model of quantum energy absorption, which exhibits this quantum-classical correspondence in the semiclassical limit.

Quantum dot spin qubits are a promising platform for realizing quantum information technologies, which can theoretically perform calculations such as factoring large integers that are otherwise intractable using classical computing methods. However, quantum dot qubit technology is still in its developmental phases, with current experimental devices capable of holding only a few (less than 10) noisy qubits. However, even with only a small number of quantum dots, interesting experiments can be performed, simulating physical systems and observing many-body phenomena which are otherwise difficult to study or numerically simulate classically.

In this thesis, we analytically examine valley states in Silicon, which is one obstacle which can potentially lead to information loss in Silicon qubits. Using a perturbative method, we calculate the dynamics of two exchange-coupled quantum dots in which there is a valley degree of freedom. We find that the spin states can become entangled with the valley states of the system if the electrons are not initialized to the correct valley states, which can adversely affect quantum computations performed on these systems. We then detail how quantum dot plaquettes can simulate the Hubbard model and give many analytic results for different magnetic phenomena that arise under this model. These results include examples of Nagaoka ferromagnetism, violations of Hund's rule, and situations where flatband ferromagnetic ground states are necessarily degenerate with nonferromagnetic states. These phenomena all require only a few quantum dots and are observable with current experimental technologies.

Complex scatterings exist in many diverse physical and real-life scenarios. Examples include atomic nuclei, quantum dots, and electromagnetic (EM) waves in resonant systems. These systems are Chaotic, meaning that minute perturbations will lead to a drastic change in the properties of the system. The underlying chaotic property makes deterministic modeling of wave properties vulnerable to small perturbations. Because of this, statistical methods play a central role in chaotic system studies. The Random Coupling Model (RCM) has been successfully applied to predicting the statistics of single chaotic EM enclosures. We here expand RCM to systems consisting of multiple volumes, and do so with highly reduced computational complexity. Going beyond knowledge-based modeling, we employ machine-learning techniques to identify hidden information in chaotic systems.

Reservoir computing (RC) is a genre of neural network. Its training is radically simplified because the input and reservoir layers stay unchanged during the process. Recent work shows that RC can reasonably predict the future evolution of spatio-temporal chaotic systems. We aim to reverse the thinking: to emulate a software RC using the spatio-temporal chaotic wave fields in physical EM enclosures. A proof-of-principle hardware RC is demonstrated experimentally.

The concept of photonic topological insulator (PTI) is translated from the study of topological insulators (TIs) in condensed matter physics. For a TI material, the charge will only flow in topologically-protected states on the boundary surrounding the material, rather than in the bulk. And thus the conductivity of the TI is topological: a bulk insulator and an edge conductor at the same time. We experimentally demonstrated a PTI system with quantum Hall (QH) and quantum spin Hall (QSH) topological phases. The TI effect also introduces a synthetic spin-1/2 degree-of-freedom to light. The Fermionic two-state property, absent in the bosonic photon world, is now accessible using the PTI system. Using PTIs, we aim to realize a chaotic system, namely the Gaussian Symplectic Ensemble (GSE) statistical group, which in principle only exists in the Fermionic world. We use simulations to show that GSE statistics will emerge in an appropriately designed PTI graph containing anti-unitary symmetry.

Lattice QCD methods provide non-perturbative access to observables in QCD. However, there are still many aspects of QCD yet to be revealed on the lattice due to the numerical difficulties called sign problems. In this talk, I will discuss recent developments on methods to alleviate or solve the real-time sign problem, which appears in Minkowski lattice calculations. Approaches to the real-time sign problem are different on classical and quantum computers, and this talk mainly focuses on classical algorithms. One well-established way to alleviate sign problems is the so-called manifold deformation method, in which one deforms the manifold of integration in the path integral to the complex plane, aiming for a milder sign problem. I will show that this method is expected to solve the real-time sign problem in bosonic lattice field theories. I will describe an algorithm based on machine learning to deform the manifold of integration toward a manifold without the sign problem. 

Theoretical physics research often requires the most advanced mathematical techniques, ranging from geometry and calculus to numerical methods and data-driven techniques used on high-performance computers. As one of the most complex and demanding sub-domains of physics nowadays, quantum information science challenges scientists to leverage and expand our toolbox in order to analyze and comprehend quantum mechanical systems. This dissertation provides a quick overview of the various hardware platforms and describes an analytical toolbox implemented in quantum information science. This toolbox contains the three most used methodologies in modern scientific research: analytical modeling, numerical simulation, and machine learning. We address historical contexts, technical specifics, application examples, and the advantages and downsides of each approach. We focus on three case studies to show the usage of this integrated analytical toolbox: First, as a qubit noise reduction study, we describe a giant atom dissipation process using a superconducting qubit coupled nonlocally to a mechanical waveguide; Second, as a quantum control optimization problem, we design a feedback cooling strategy based on a toy model of weakly monitored Bose-Einstein condensates. At last, as an image data analysis, we employ neural network architectures to classify and analyze our experimental dataset automatically.

Interest in correlated electron states in strongly correlated materials, such as transition metal dichalcogenides (TMDs), has been growing in recent years thanks to significant technological advancements in cryogenic quantum optics measurement techniques that allow for their experimental realization. Milli-kelvin temperatures are required to eliminate thermalization effects that otherwise mask the interesting correlated physics in these materials. In an effort to contribute to the understanding of these states, we developed an ultra-low temperature dilution refrigerator measurement system with free-space optical access that is able to achieve a base temperature of  <30 milli-kelvin and apply a ±12 T perpendicular magnetic field. We utilize a 100x cryogenic objective with 0.82 NA to make highly localized optical measurements on our samples. Our custom stage system allows for quick sample exchange and rapid characterization of our devices.

TMDs have been shown to be suitable materials for probing new and interesting exciton physics. In monolayer form, their direct band gap in the visible range and high binding energies open the possibility to optically explore higher energy Rydberg states. As the understanding of the neutral exciton's Rydberg series has grown in recent years, interest has started to shift toward the less understood charged excitons.  Using photoluminescence excitation (PLE), we sweep a laser's energy  across the spectral range of the n>1 Rydberg exciton states and monitor the emission intensities of the 1s excitons. Through this technique, we were able to measure the precise spectral profile and carrier density dependence of the 3s neutral (X₀^3s), 2s neutral (X₀^2s ), and 2s negatively charged (X_-^2s) excitons in monolayer WSe₂. By applying a perpendicular magnetic field to the sample, we were also able to measure the valley dependent Zeeman splitting of both X₀^2s and X_-^2s and extracted their corresponding g-factors.

A Josephson junction (JJ) is known as a weak link connecting two superconductors, in which the non-dissipative supercurrent flows. More than two superconductors also can form a single composite JJ, called a “multi-terminal JJ”, by being connected through a common weak link. The supercurrent in multi-terminal JJs may depend on multiple superconducting phase differences defined across the junction, which is attributed to the supercurrent-carrying sub-gap quasiparticle bound states called Andreev bound states (ABSs).

In this dissertation, we first investigate the supercurrent of three- and four-terminal JJs fabricated on hybrid two-dimensional Al/InAs (superconductor/semiconductor) heterostructures. We define the critical current of an N-terminal junction as a (N − 1)-dimensional hypersurface of the bias currents, which can be reduced to a set of critical current contours (CCCs) in the two-dimensional planes. The geometry of the CCCs are modified non-trivially in response to magnetic field, electrical gating and phase biasing, which is attributed to the multi-phase-dependent ABSs. We also show that our experimental observations are consistent with quantum transport simulations based on a tight-binding model of the hybrid superconductor/semiconductor system. Second, we demonstrate the multi-phase-dependence of ABSs in three-terminal JJs by tunneling spectroscopy measurements. The ABS energy spectrum mimics electronic band structure in solid, which makes multi-terminal JJs provide a new platform to study band topology in higher dimensional parameter space. Moreover, spin-splitting of ABS energies induced by the multi-phase and gapless energy spectrum facilitated by the presence of a discrete vortex, a nonzero winding of the superconducting phases, are investigated.

Monolayer two-dimensional transition metal dichalcogenides (2D TMDs) represent a class of atomically thin semiconductors with unique optical properties. Similar to graphene, but with a three-layer (staggered) honeycomb lattice, TMDs host direct-gap transitions at their ±K valleys that exhibit circular-dichroism due to their finite Berry curvature. The reduced dimensionality of materials in this system, combined with large effective carrier masses, leads to enhanced Coulomb interaction and extremely tightly bound excitons (E_B ≈ 150-300 meV). Here, we seek to exploit the unusually tight binding of the excitons to probe two different types of higher energy exciton species in TMDs.

First, we experimentally probe the magneto-optical properties of 2s Rydberg exciton species in WSe₂. The magnetic response of excitons gives information on their spin and valley configurations, nuanced carrier interactions, and insight into the underlying band structure. Recently, there have been several reports of 2s/3s charged excitons in TMDs, but very little is still known about their response to external magnetic fields. Using photoluminescence excitation spectroscopy, we verify the 2s charged exciton and report for the first time its response to an applied magnetic field. We benchmark this response against the neutral exciton and find that both the 2s neutral and charged excitons exhibit similar behavior with $g$-factors of   and , respectively.

Second, via theoretical calculations, we investigate the exciton spectrum generated in 2D semiconductors under illumination by twisted light. Twisted light carries orbital angular momentum (OAM) which can act as an additional tunable degree of freedom in the system. We demonstrate that twisted light does not have the ability to modify the exciton spectrum and induce dipole-forbidden excitons, in contrast to atoms. This result stems from the fact that the additional OAM is transferred preferentially to the center-of-mass (COM) of the exciton, without modifying the relative coordinate which would allow dipole-forbidden higher energy excitons to form.

Cell motility plays an integral role in most biological processes. One principle of motility is the protrusions and retractions of cellular membranes called pseudopods. The physical force behind pseudopod formation is actin polymerization. As the physical driver, actin polymerization integrates the cells' upstream biochemical signaling cascades and turns the signals into action as the combined output and readout of the state of the cell. Actin polymerization not only occurs within pseudopods but propagates throughout a cell in waves that can be understood and modeled as excitable media.

This dissertation focuses on actin wave dynamics in the context of directed cell migration using both experimental and numerical techniques. Directed cell migration is essential in physiological processes including embryonic development, cancer metastasis, and wound healing. In this thesis, I analyze how immune-like cells are guided by external stimuli that are common in wound environments: electric fields, chemical gradients, and surface texture. A focus of this work is on the emergent excitable wave behavior of actin, and the pseudopods they generate, in simplified, in vitro environments.

Actin waves have been previously shown to respond to and be guided by the topography of an underlying substrate. Additionally, static quantifications of actin filaments after electric field stimulation become asymmetrically distributed within the cytoplasm. In neutrophils, the combination of cues leads to higher control of cell motility by guiding the internal actin waves. Using an optical flow algorithm, I quantify the actin waves on multiple length scales to ascertain the role of each guidance cue in affecting cell motion. I find that the waves preferentially polymerize and travel along the nanoridge length. Actin waves nucleate preferentially on the cathode side and reorient the cells axis of polarity (i.e., the position of the dominant pseudopod).

The second example of competing guidance cues involves studying the collective motion of cells in response to cell-cell signal relay in competition with surface topography. We use Dictyostelium discoideum cells as a model system for this work, as they migrate collectively due to signal relay. The signal relay of these cells is similar to many immune cell species. Using a combination of image analysis tools and a coarse-grained stochastic model, we find that guidance by nanoridges overrides the chemical signal relay and forces cells to migrate individually, suppressing streaming behavior. We model both the secretion and propagation of chemical signals using an excitable systems framework. This work highlights that bidirectional signals can be effective at suppressing cell-cell attraction and streaming motion.

The response of immune cells to external stimuli in the wound environment is not universal. Macrophages---one of the largest immune cells---are observed to migrate in the opposite direction of the wound upon wound-induced electric field generation. In the third example, I study actin dynamics of M0 (resting) macrophage cells to elucidate the method in which these cells interact with external electric fields. This cell system exhibits oscillatory actin waves at rest. With electric field stimulation, the oscillatory actin waves start to generate protrusions. Without oscillations, the protrusions begin with actin-depleted regions, indicating that contractile elements are involved. This section highlights the different methods in which actin waves integrate external cues into cell responses in different biological contexts.

The BaAl₄-type structure hosts a variety of interesting and exotic properties, with descendant crystal structure resulting numerous interesting ground states of matter including magnetic, super-conducting and strongly correlated electron phenomena. BaAl₄ itself has recently been shown to host a non-trivial topological band structure but is otherwise a paramagnetic metal. However, the other members of the 1-4 family, such as SrAl₄ and EuAl₄, exhibit symmetry-breaking ground states including charge density wave (CDW) and magnetic order, respectively. SrAl₄ hosts a second transition at 94K that is hysteretic in temperature and is a structural transition to a monoclinic structure. Here I report on the charge density wave in SrAl₄ and the effect of the structural transition on the physical and electronic properties of the material. The structural transition is extremely subtle with deviation of around 0.5 degrees from the tetragonal structure but shows significant changes resistivity, hall and magnetic susceptibility measurements. This transition is extremely sensitive to disorder and can be suppressed completely by substituting 1% Ba nominally or using less pure Sr during crystal growth. Furthermore, magnetoresistance in this material is extremely large, and can be up to 140 times at 2K. A combination of magnetoresistance and hall measurements are used to fit the data to a two band model to extract carrier density and mobility of the charge carriers at 2K. Finally, work was done on the evolution of the charge-ordered state in high quality single crystals of the solid solution series Ba_1−xSr_xAl₄, using transport, thermodynamic and scattering experiments to track the 243 K CDW order in SrAl₄ as it is suppressed with Ba substitution until its demise at x =0.5. Neutron and x-ray diffraction measurements reveal a nearly commensurate CDW state in SrAl₄ with ordering vector (0,0,0.097) that evolves with Ba substitution to (0,0,0.18) and (0,0,0.21) for x=0.8 and x=0.55, respectively. DFT calculations show a softening of phonons in SrAl₄ hinting at EPC strength being the source of the charge order in this material. Similar calculations are done on the Ba substitutions to investigate the nature of the charge density waves. With very little change in the lattice parameters in this series, this evolution raises important questions about the nature of the electronic structure that directs a dramatic change in charge ordering.

We consider the challenging problem of forecasting high-dimensional, spatiotemporal chaotic systems. We are primarily interested in the problem of forecasting the dynamics of the earth's atmosphere and oceans, where one seeks forecasts that (a) accurately reproduce the true system trajectory in the short-term, as desired in weather forecasting, and that (b) correctly capture the long-term ergodic properties of the true system, as desired in climate modeling. We aim to leverage two types of information in making our forecasts: incomplete scientific knowledge in the form of an imperfect forecast model, and past observations of the true system state that may be sparse and/or noisy. In this thesis, we ask if machine learning (ML) and data assimilation (DA) can be used to combine observational information with a physical knowledge-based forecast model to produce accurate short-term forecasts and consistent long-term climate dynamics.

We first describe and demonstrate a technique called Combined Hybrid-Parallel Prediction (CHyPP) that combines a global knowledge-based model with a parallel ML architecture consisting of many reservoir computers and trained using complete observations of the system's past evolution. Using the Kuramoto-Sivashinsky equation as our test model, we demonstrate that this technique produces more accurate short-term forecasts than either the knowledge-based or the ML component model acting alone and is scalable to large spatial domains. We further demonstrate using the multiscale Lorenz Model 3 that CHyPP can incorporate the effect of unresolved short-scale dynamics (subgrid-scale closure).

We next demonstrate how DA, in the form of the Ensemble Transform Kalman Filter (ETKF), can be used to extend the Hybrid ML approach to the case where our system observations are sparse and noisy. Using a novel iterative scheme, we show that DA can be used to obtain training data for successive generations of hybrid ML models, improving the forecast accuracy and the estimate of the full system state over that obtained using the imperfect knowledge-based model.

Finally, we explore the commonly used technique of adding observational noise to the ML model input during training to improve long-term stability and climate replication. We develop a novel training technique, Linearized Multi-Noise Training (LMNT), that approximates the effect of this noise addition. We demonstrate that reservoir computers trained with noise or LMNT regularization are stable and replicate the true system climate, while LMNT allows for greater ease of regularization parameter tuning when using reservoir computers.

A search for emerging jets produced in proton-proton collisions at a center-of-mass energy of 13 TeV is presented in this thesis. This search examines a hypothetical dark QCD sector that couples to the standard model (SM) through a scalar mediator. The scalar mediator decays into a standard model quark and a dark sector quark. As the dark sector quark showers and hadronizes, it produces long-lived dark mesons that subsequently decay into SM particles, resulting in a jet with multiple displaced vertices, known as an emerging jet. This search extends the existing efforts using data collected with the CMS detector by including the possibility of a flavored coupling between the standard model sector and dark sector, which results in emerging jets containing both long-lived and prompt decays. This search looks for pair production of the scalar mediators at the large hardon collider, yielding events with two SM jets and two emerging jets.

As the detector signature left by such dark sector showers significantly deviates from the assumptions made when designing the CMS detector, a fully data-based method is used for evaluating the number of standard model events that can be mistaken as signal events. The data-based method works by comparing the probability of standard model jets being misidentified as emerging jets in a signal-free data set and then using this probability to calculate a per-event weighting factor applied to compare events in the signal-depleted region. The weighted sum can be used to estimate the standard model number of events that enter a signal-enriched region.

The search is carried out on data collected by the CMS experiment corresponding to an integrated luminosity of 138/fb . No significant excess over the expected background is observed. The results are interpreted using two dark sector models and exclude mediator masses up to 1750 GeV for an unflavored dark QCD model and up to 2000 GeV for a flavor-aligned dark QCD model.

Since its inception in the early 1920s, the theory of quantum mechanics has provided a framework to describe the physics of nature; or at least our interpretations about systems in nature. However, even though quantum theory works, the unsettling question of ``why?' still remains. The field of quantum information science and technology (QIST) has brought together a collection of disciplines forming a united multidisciplinary collaborative effort towards realizing a large-scale quantum processor as an attempt to understand quantum mechanics better. It has been established in the field that the most efficient architectural design of this quantum processor would be composed of numerous individual quantum computers, quantum simulators, quantum networks, quantum memories, and quantum sensors that are ``wired'' together creating just the hardware layer in the full stack of the machine. Realizing a module-based quantum processor on such a macroscopic scale is an ongoing and challenging endeavor in itself.

However, existing noisy intermediate-scale quantum (NISQ) devices across all the quantum applications above are still worth building, running, and studying. NISQ quantum computers can still provide quantum advantages over classical computation for given algorithms, and quantum simulators can still probe complex many-body dynamics that remain improbable to consider even on the best supercomputer. One such system is the trapped-ion quantum simulator at the center of this dissertation. Using ¹⁷¹Yb⁺ ions, we expand our “analog” quantum simulation toolbox by incorporating “digital” quantum computing techniques in each of the three experiments presented in this work.

In the first experiment, we perform a quantum approximate optimization algorithm (QAOA) to estimate the ground-state energy of a transverse-field antiferromagnetic Ising Hamiltonian with long-range interactions. For the second project, we develop and demonstrate dynamically decoupled (DD) quantum simulation sequences in which the coherence in observed dynamics evolving under the unitary operator of the target Hamiltonian is extended while the known noise is suppressed. Finally, in the third project, we implement an experimental protocol to measure the spectral form factor (SFF) and its generalization, the partial spectral form factor (PSFF), in both an ergodic many-body quantum system and in a many-body localized (MBL) model. Consequently, a quantum simulator can be utilized to test universal random matrix theory (RMT) predictions, and simultaneously, probe subsystem eigenstate thermalization hypothesis (ETH) predictions of a quantum many-body system of interest.