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.