Magnetic reconnection is a widespread process in plasma physics that is crucial for the rapid release of magnetic energy and is believed to be a key factor in generating non-thermal particles in space and various astrophysical systems. In this dissertation, a set of equations are developed that extend the macroscale magnetic reconnection simulation model kglobal to include particle ions. The extension from earlier versions of kglobal, which included only particle electrons, requires the inclusion of the inertia of particle ions in the fluid momentum equation. The new equations will facilitate the exploration of the simultaneous non-thermal energization of ions and electrons during magnetic reconnection in macroscale systems. Numerical tests of the propagation of Alfvén waves and the growth of firehose modes in a plasma with anisotropic electron and ion pressure are presented to benchmark the new model. The results of simulations of magnetic reconnection accompanied by electron and proton heating and energization in a macroscale system are presented. Both species form extended powerlaw distributions that extend nearly three decades in energy. The primary drive mechanism for the production of these nonthermal particles is Fermi reflection within evolving and coalescing magnetic flux ropes. While the powerlaw indices of the two species are comparable, the protons overall gain more energy than electrons and their powerlaw extends to higher energy. The power laws roll into a hot thermal distribution at low energy with the transition energy occurring at lower energy for electrons compared with protons. A strong guide field diminishes the production of non-thermal particles by reducing the Fermi drive mechanism. In solar flares, proton power laws should extend down to 10's of keV, far below the energies that can be directly probed via gamma-ray emission. Thus, protons should carry much more of the released magnetic energy than expected from direct observations.

In Encounter 14 (E14), the Parker Solar Probe encountered a reconnection event in the heliospheric current sheet (HCS) that revealed strong ion energization with power law distributions of protons extending to 500keV. Because the energetic particles were streaming sunward from an x-line that was anti-sunward of PSP, the reconnection source of the energetic ions was unambiguous. Using upstream parameters based on the data observed by PSP, we simulate the dynamics of reconnection applying kglobal and analyze the resulting spectra of energetic electrons and protons. Power law distributions extending nearly three decades in energy develop with proton energies extending to 500keV, consistent with observations. The significance of these results for particle energization in the HCS will be discussed.

Quantum computing holds vast potential for solving classically hard problems. While large-scale fault-tolerant quantum computers capable of these tasks are still in the future, small and noisy prototypes have been demonstrated on several candidate platforms. Among these, trapped ion qubits have been at the forefront of quantum computing because of their long coherence times, high-fidelity quantum gates, and all-to-all connectivity. This dissertation investigates efficient ways to utilize quantum resources on a trapped ion quantum computers (TIQC) at the interface between theory and experiment.

The Quantum Approximate Optimization Algorithm (QAOA) can solve graph combinatorial optimization problems by applying multiple rounds of variational circuits. We experimentally show that QAOA results improve with deeper circuits for multiple problems on several arbitrary graphs on a TIQC. We also demonstrate QAOA with a novel mixer which allows fair sampling of all optimal solutions in weighted problems.

We propose and demonstrate a high-fidelity and resource-efficient scheme for driving simultaneous entangling gates in trapped-ion chains. We show the advantage of parallel operation with a simple digital quantum simulation where parallel gates improves the overall fidelity significantly.

Accurate knowledge about quantum noise in real devices can inform hardware design as well as enable the co-design of tailored quantum error correction codes. Noise characterization is a challenging task due to the computational cost. We test an ancilla-assisted Pauli noise learning protocol that uses a sample size linear to the system size. We also design and demonstrate a method to improve its performance by reducing ancilla noise in post-processing.

Quantum computing promises applications in physics, cryptography, material science, pharmaceuticals, and a wide range of other science. Superconducting qubits are a possible platform for developing a quantum computer. To perform useful quantum computations, the coherence and control of superconducting qubits must be greatly improved. In this dissertation, I discuss two main results to improve the performance of transmon qubits.

For the first project, I fabricated and characterized the coherence of transmon devices with asymmetric superconducting gaps. Previous models suggested that devices with asymmetric superconducting gaps on either side of the Josephson junction should be resilient to loss from quasiparticle tunneling. To gap-engineer the Josephson junctions, I used Ti metal to proximitize and lower the superconducting gap of the Al counter-electrode.

Unfortunately, the energy relaxation time constant for an Al/AlOx/Al/Ti 3D transmon was T₁ = 1μs, over two orders of magnitude shorter than the measured T₁ = 134μs of an Al/AlOx/Al 3D transmon with Al capacitor pads and the measured T₁ = 143μs of an Al/AlOx/Al 3D transmon with Ta capacitor pads. DC IV measurements of proximitized Josephson junctions showed a reduced superconducting gap, demonstrating that the gap-engineering in the Al/Ti layer was successful. However, these same IV measurements measured greatly increased excess current for voltage biases below the superconducting gap than in standard Al/AlOx/Al junctions. This suggests the addition of Ti caused the junction quality to worsen, potentially being a source of tunneling loss in the transmon devices. Intentionally adding oxygen disorder between the Al and Ti layers reduced the proximity effect and subgap current in DC measurements while increasing the relaxation time of a 3D transmon to T₁ = 32μs.

Additionally, I designed an Al/AlOx/Al SQUID device to perform DC IV measurements of junctions with tunable total critical current. In a single junction, subgap tunneling features can be due to the critical current interacting with the environment, subgap quasiparticle processes, or other sources. Reducing the critical current allows these features to be differentiated and more accurately measure the effects from quasiparticle tunneling alone.

Characterizing this device showed subgap tunneling features consistent with inelastic Cooper pair tunneling and quasiparticle transport via multiple Andreev reflection in a low transparency junction. This measurement technique could be used to further study gap-engineered junctions.

For the second project, I characterized a 2D Ta transmon device and performed high-fidelity single qubit gates. First, I used error amplifying pulse sequences to fine-tune the qubit gate pulses. I estimated the resulting gate error with randomized benchmarking. The total error of gates with Gaussian and cosine shaped pulses were characterized at a variety of pulse lengths. Analyzing the pulse envelopes in the frequency domain and directly measuring leakage to the transmon's second excited state revealed that leakage from driving higher qubit transitions was a major source of gate error. Next, I characterized gates using a pulse shape designed by a physics informed neural network and found improved gate error for 16~ns pulses achieving an average error per gate of (3.36±0.03)×10⁻⁴ compared to (5.54±0.24)×10⁻⁴ for a cosine shaped pulse and (3.93±0.12)×10⁻⁴ for a Gaussian shaped pulse of the same length. Further optimization of the pulse using predistortion or leakage reduction strategies may yield even greater performance.

Pulsars are highly magnetized rotating neutron stars known for their periodic bursts of radio emission. Decades of astronomical observations revealed that pulsars produce non-thermal radiation in all energy bands, from radio to gamma rays, covering more than 20 decades in photon energy. Modern theories consider strongly magnetized relativistic electron-positron plasmas to be the source of the observed emission. In my Thesis, I investigate physical processes that can be responsible for plasma production and the observed high-energy emission in the wide range of photon energies, from eV to TeV.

In the first Chapter of my Thesis, I investigate relativistic magnetic reconnection with strong synchrotron cooling using three-dimensional particle-in-cell kinetic plasma simulations. I characterize the spectrum of accelerated particles and emitted synchrotron photons for varying strengths of synchrotron cooling. I show that the cutoff energy of the synchrotron spectrum can significantly exceed the theoretical limit of 16 MeV if the plasma magnetization parameter exceeds the radiation reaction limit. Additionally, I demonstrate that a small fraction of ions present in the current sheet can be accelerated to the highest energies, making relativistic radiative reconnection a promising mechanism for the acceleration of high-energy cosmic rays.

In the second Chapter, I present the first multi-dimensional simulations of the QED pair production discharge that occurs in the polar region of the neutron star. This process is believed to be the primary source of the pair plasma in pulsar magnetospheres and also the source of the radio emission. In this work, I focus on the self-consistently emerging synchronization of the discharges in different parts of the polar region. I find that pair discharges on neighboring magnetic field lines synchronize on a scale comparable to the height of the pair production region. I also demonstrate that the popular “spark” model of pair discharges is incompatible with the universally adopted force-free magnetospheric model: intermittent discharges fill the entire polar region that allows pair production, leaving no space for discharge-free regions. My findings disprove the key assumption of the spark model about the existence of distinct discharge columns.

In the third Chapter, I demonstrate how the key findings of two previous chapters can provide a self-consistent explanation of the recently discovered very-high-energy, reaching 20TeV, pulsed emission in Vela pulsar. Motivated by the results of recent global simulations of pulsar magnetospheres, I propose that this radiation is produced in the magnetospheric current sheet undergoing radiative relativistic reconnection. I show that high-energy synchrotron photons emitted by reconnection-accelerated particles efficiently produce electron-positron pairs. The density of secondary pairs exceeds the supply from the polar cap and results in a self-regulated plasma magnetization parameter of ~10^7. Electrons and positrons accelerate to Lorentz factors comparable to  ~10^7 and emit the observed GeV radiation via the synchrotron process and ~10 TeV photons by Compton scattering of the soft synchrotron photons emitted by secondary pairs. My model self-consistently accounts for the ratio of the gamma-ray and TeV luminosities.

Topological photonics has emerged in recent years as a powerful paradigm for the design of photonic devices with novel functionalities. These systems exhibit chiral or helical edge states that are confined to the boundary and are remarkably robust against certain defects and imperfections. While several applications of topological photonics have been demonstrated, such as robust optical delay lines, quantum optical interfaces, lasers, waveguides, and routers, these have largely been proof-of-principle demonstrations. In this dissertation, we present the design and generation of the first topological frequency comb. While on-chip generation of optical frequency combs using nonlinear ring resonators has led to numerous applications of combs in recent years, they have predominantly relied on the use of single-ring resonators. Here, we combine the fields of linear topological photonics and frequency microcombs and experimentally demonstrate the first frequency comb of a new class in an array of hundreds of ring resonators. Through high-resolution spectrum analysis and out-of-plane imaging we confirm the unique nested spectral structure of the comb, as well as the confinement of the parametrically generated light. Additionally, we present a theoretical study of a new kind of valley-Hall topological photonic crystal that utilizes a position dependent perturbation (or “mass-term”) to manipulate the width of the topological edge modes. We show that this approach, due to the inherent topological robustness of the system, can result in dramatic changes in mode width over short distances with minimal losses. Additionally, by using a topological edge mode as a waveguide mode, we decouple the number of supported modes from the waveguide width, circumventing challenges faced by more conventional waveguide tapers. 

Metamaterials are artificial structures consisting of sub-wavelength ‘atoms’ with engineered electromagnetic properties that create exotic light-matter interactions through the effective medium approximation. Since the early 2000s, superconductors have been incorporated into a variety of structures to achieve tunable, low-loss, and nonlinear metamaterials, and have enabled applications such as negative index of refraction, near zero permittivity, and parametric amplification. We have designed, fabricated and characterized two types of superconducting metamaterials based on the quantum three-junction flux qubits and classical radio frequency superconducting quantum interference devices (rf SQUIDs).

The coplanar waveguide resonators hosting the qubit meta-atoms exhibit anomalous reduction in loss in microwave transmission measurements at low rf excitation levels upon decreasing temperature below 40 mK. In contrast, the well-known standard tunneling model (STM) of the two-level systems (TLS), believed to be the dominant source of loss at low temperatures, predicts a loss increasing then saturating with lowering temperatures. This anomalous loss reduction is attributed to the discrete nature of the TLS ensemble in the resonator. As temperature decreases, the individual TLS response bandwidth reduces with their coherence rate Γ₂ ~ T, creating less overlap between neighboring TLS in the energy spectrum. This effective reduction in the density of states around the probe frequency is responsible for the observed lower loss at low rf excitation levels and low temperatures as compared to the STM prediction. We also incorporate the discrete TLS ansatz with the generalized tunneling model proposed by Faoro and Ioffe [PRL 2012, 109, 157005 and PRB 2015, 91, 014201] to fit the experimental data over a wide range of temperatures and rf excitation powers. The resulting goodness of fit is better than all common alternative explanations for the observed phenomenon.

 Large metamaterial arrays of hysteretic (β_rf=L_geo/L_JJ > 1) classical rf SQUIDs are also designed and characterized in microwave transmission measurements, where we observed the SQUID self-resonances tuning with applied dc and rf magnetic flux, as well as temperature. The resonance features are tuned with dc flux in integers of the flux quantum, as expected. Due to the phenomenon of multistability present in the large system, the resonance bands can cross those from adjacent dc flux periodicities resulting in hysteresis in dc flux sweeps, which is observed in the experiment. Furthermore, we developed a new three-dimensional architecture of rf SQUID metamaterials where the nearest-neighbor SQUID loops overlap. The resulting capacitive coupling dramatically changes the response by introducing many more resonance bands that spread over a broad range of frequencies, the upper limit of which is much higher than the single-layer counterparts. A resistively and capacitively shunted junction (RCSJ) model with additional capacitive coupling between SQUIDs is proposed and successfully attributes the high frequency bands to the displacement current loops formed between the overlapping wiring of neighboring SQUIDs. The capacitively-coupled rf SQUID metamaterial is relevant to the design of single-flux-quantum-based superconducting digital electronic circuits, which has adopted three-dimensional wiring to reduce the circuit footprint.

The Standard Model (SM) of particle physics has been extremely successful in describing the interactions of electromagnetic, weak nuclear, and strong nuclear forces. Yet, there are both unexplained phenomena and experimentally observed tensions with the SM, motivating searches for new physics (NP).

Collider experiments typically perform two kinds of analyses: direct searches for new physics and precision measurements of SM observables. For example, experimental collaborations use collider data to search for NP particles like the heavy superpartners of the SM particles, whose observation would be clear evidence of supersymmetry (SUSY). These direct searches often consider kinematic regions where the SM background is small. This strategy is unable to probe regions of the NP parameter space where the SM background is dominant.

The same collaborations also measure the masses of SM particles, which not only serve as consistency tests of the SM, but can also probe effects of NP. In 2022, the Collider Detector at Fermilab (CDF) collaboration published the most precise measurement of the W boson mass: m_W = 80433.5 ± 9.4 MeV. This measurement is in 7𝜎 significance tension with the SM prediction via the electroweak (EW) fit, m_W^pred. = 80354 ± 7 MeV. Many extensions to the SM can affect the prediction of m_W with indirect effects of heavy NP. However, in 2023, the ATLAS re-measurement of the W boson mass, m_W = 80360 ± 16 MeV, was found to be consistent with the SM prediction. Both collaborations found a high-precision agreement between the measured kinematic distributions and the SM prediction of the kinematic distributions for their corresponding extracted m_W.

We propose using the precision measurements of m_W to directly probe NP contributing to the same final state used to measure m_W: a single charged lepton (l) and missing transverse energy (MET). This strategy is independent of modifying the EW fit, which tests indirect effects of NP on the predicted value of m_W. Any NP producing l+MET which modifies the kinematic distributions used to extract m_W can be probed with this method. An important point of this strategy is that since these distributions are used to search for NP while measuring m_W, a simultaneous fit of NP and SM parameters, thus unifying searches and measurements. This simultaneous fitting can induce a bias in the measured m_W, but only to a limited extent for our considered models.

We consider three categories of NP which can be probed: (i) modified decay of W bosons; (ii) modified production of W bosons; and (iii) l+MET scenarios without an on-shell W boson. We also show that models whose signals extend beyond the kinematic region used to measure m_W can be probed in an intermediate kinematic region. Our results highlight that new physics can still be directly discovered at the LHC, including light new physics, via SM precision measurements. Additionally, anticipated improvements in precision SM measurements at the High Luminosity LHC further enables new searches for physics Beyond the Standard Model (BSM).

Statistical learning is emerging as a new paradigm in science.

This has ignited interest within our inherently quantum world in exploring quantum machines for their advantages in learning, generating, and predicting various aspects of our universe by processing both quantum and classical data. In parallel, the pursuit of scalable science through physical simulations using both digital and analog quantum computers is rising on the horizon.

In the first part, we investigate how physics can help classical Artificial Intelligence (AI) by studying hybrid classical-quantum algorithms. We focus on quantum generative models and address challenges like barren plateaus during the training of quantum machines. We further examine the generalization capabilities of quantum machine learning models, phase transitions in the over-parameterized regime using random matrix theory, and their effective behavior approximated by Gaussian processes.

In the second part, we explore how AI can benefit physics. We demonstrate how classical Machine Learning (ML) models can assist in state recognition in qubit systems within solid-state devices. Additionally, we show how ML-inspired optimization methods can enhance the efficiency of digital quantum simulations with ion-trap setups

Finally, in the third part, we focus on how physics can help physics by using quantum systems to simulate other quantum systems. We propose native fermionic analog quantum systems with fermion-spin systems in silicon to explore non-perturbative phenomena in quantum field theory, offering early applications for lattice gauge theory models.

Since the discovery of the Higgs boson (H) with a mass of 125 GeV by the ATLAS and CMS collaborations at CERN LHC in 2012, the focus of the particle physics community has shifted towards precise measurements of its properties and so far the measurements align with the standard model (SM) predictions. Among the properties, of particular interest is the Higgs trilinear self-coupling, which can be directly measured through the production of the Higgs boson pair (HH).

This thesis presents three analyses using proton-proton collision data at sqrt(s) = 13 TeV with an integrated luminosity of 138 fb−1: a search for SM Higgs boson pair production with one associated vector boson (VHH), a combination of H measurements and HH searches, and a search for a new particle decaying to a W boson and a photon (γ).

The VHH search focuses on Higgs bosons decay to bottom quarks with a novel background estimation approach. The combination of H measurements and HH searches aims to constrain the trilinear self-coupling with the best possible precision. The Wγ resonance search focuses on leptonic W decays, achieving the best sensitivity in the mass ranges considered compared to other searches for this resonance. 

Achieving control over light-matter interactions is crucial for developing quantum technologies. This dissertation discusses two novel demonstrations where chiral light was used to control light-matter interaction in fermionic quantum Hall systems. In the first work, we demonstrated the transfer of orbital angular momentum from vortex light to itinerant electrons in quantum Hall graphene. In the latter, we demonstrated circular-polarization-dependent strong coupling in a 2D gas in the quantum Hall regime coupled to a microcavity. Our findings demonstrate the potential of chiral light to control light-matter interactions in quantum Hall systems.

In the first part of this dissertation, we review our experimental demonstration of light-matter interaction beyond the dipole-approximation between electronic quantum Hall states and vortex light where the orbital angular momentum of light was transferred to electrons. Specifically, we identified a robust contribution to the radial photocurrent, in an annular graphene sample within the quantum Hall regime, that depends on the vorticity of light. This phenomenon can be interpreted as an optical pumping scheme, where the angular momentum of photons is transferred to electrons, generating a radial current, where the current direction is determined by the vorticity of the light. Our findings offer fundamental insights into the optical probing and manipulation of quantum coherence, with wide-ranging implications for advancing quantum coherent optoelectronics.

In the second part of this dissertation, we review our experimental demonstration of a selective strong light-matter interaction by harnessing a 2D gas in the quantum Hall regime coupled to a microcavity. Specifically, we demonstrated circular-polarization dependence of the vacuum Rabi splitting, as a function of magnetic field and hole density. We provide a quantitative understanding of the phenomenon by modeling the coupling of optical transitions between Landau levels to the microcavity. This method introduces a control tool over the spin degree of freedom in polaritonic semiconductor systems, paving the way for new experimental possibilities in light-matter hybrids.

Driven systems have been of particular interest in the field of ultracold atomic gases. The precise control and relative purity allow for construction of many novel Hamiltonians. One such system is the ‘breathing’ lattice, where both the frequency and amplitude is modulated in time, much like an accordion. We present the results of a phenomenological investigation of a proposed experiment, one where we apply a ‘two-frequency’ breathing lattice to an atomic system. Our results show a shift in the tunneling Hamiltonian away from nearest neighbour couplings. 

The nitrogen-vacancy (NV) center is a photostable fluorescent atomic defect in diamond, exhibiting unique magneto-optic effects. Its Hamiltonian is sensitive to the local magnetic, electric field, temperature, and strain, making NV centers ideal for atomic-scale quantum sensing and various scientific and technological applications. In this thesis, we first briefly introduce the properties and applications of nitrogen-vacancy centers, then we present a cost-effective method for fabricating and characterizing a new class of durable, highly integrated scanning quantum sensors using both fiber-based and cantilever-based nitrogen-vacancy center scanning probes using nanodiamonds.

The fiber-based NV center scanning probe is compatible with any tuning fork-based scanning probe microscope and supports multiple operational modes, including near-field excitation with far-field detection, far-field excitation with near-field detection, near-field excitation with near-field detection and far-field excitation with far-field detection. These diverse functional modes enable high-sensitivity and high-resolution quantum imaging and sensing applications, such as magnetic field imaging, electric field imaging, and thermal imaging at the nanoscale.

The cantilever-based nitrogen-vacancy centers scanning probe is suitable for use with any commercial cantilever-based scanning probe microscopes and it allows highly integrated microwave manipulation through metal coating. Additionally, we have developed a methodology to accurately determine the orientation of NV centers beneath the tip, establishing a foundation for utilizing these unique NV scanning probe for quantum sensing. Compared to existing fabrication methods, our method is reproducible, low-cost, and robust, offering significant advancements in NV center scanning probe technology.

Advances in imaging and biological sample preparations now allow researchers to study collective behavior in cellular networks with unprecedented detail. Imaging the electrical signaling of neuronal networks at the cellular level has generated exciting insights into the multiscale interactions within the brain. Detailing such interactions reveals the specifically electrical information processing performed by the brain. This thesis aims at a complementary view of the general information processing of the brain, focusing on other modes of information. The modes discussed are the collective, dynamical characteristics of non-electrically active, non-neuronal brain cells, and mechanical systems. Astrocytes are such brain cells, and the cytoskeleton is a dynamic, mechanical system of various filamentous networks. The two filamentous networks studied herein are the actin cytoskeleton, and the microtubule network. Techniques from calcium imaging and cell mechanics are adapted to measure these often overlooked information channels, which operate at length and timescales distinct from electrical information transmission. Inclusion of the collective dynamics of both astrocytes and the cytoskeleton into brain networks is a step toward a fuller characterization of brain functioning and cognition.

Computer vision and information theory are used on structural, astrocyte actin images, microtubule structural image sequences, and the calcium signals of collections of astrocytes. Filamentous alignment of actin with nearby boundaries reveals that stellate astrocytes have more perpendicularly oriented actin than undifferentiated astrocytes. Harnessing the larger length scale and slower dynamical time scale of microtubule filaments, relative to actin filaments, led to the creation of a computer vision tool to measure lateral filamentous fluctuations. Finally, we adapt information theory to the slow calcium Ca²⁺ signals within astrocyte networks classified according to subtype. Despite multiple physiological differences with immature and injured astrocytes, stellate (healthy) astrocytes have the same speed of information transport as these other astrocyte subtypes. This uniformity in speed persists when either the cytoskeleton (latrunculin B) or energy state (ATP) is perturbed. Astrocytes, regardless of physiological subtype, tend to behave similarly when active under normal conditions. However, these healthy astrocytes respond most significantly to cytoskeletal and energy perturbation, relative to immature and injured astrocytes, as seen within their pairwise interactions and individual calcium fluctuations as measured by mutual information and cross correlation, and partitioned entropy, respectively.

These results indicate the value of drawing information from structure and dynamics. We developed and adapted tools across scales from nanometer scale alignment of actin filaments to hundreds of microns scale information dynamics in astrocyte networks. This work highlights the importance of investigating all potential modalities of information within complex biological systems.

In recent years, many advancements in astrophysics have brought astrophysicists new tools to study the universe. Specifically, the discovery of astrophysical neutrino by IceCube Neutrino Observatory and Gravitational wave by LIGO/Virgo collaboration has started the era of multi-messenger astronomy. Scientists can finally use messengers other than electromagnetic waves to study astrophysical phenomena.With the addition of new messengers, it is crucial that data from multiple instruments and messengers can be jointly analyzed through a unified framework using one physics model. In this work, we present a method to jointly analyze data from HAWC Gamma-ray Observatory and IceCube Neutrino Observatory by using a newly developed IceCube likelihood software called i3mla and the existing HAWC likelihood software called HAL. Together with the Multi-Mission Maximum Likelihood framework (3ML), we can jointly fit the gamma-ray emission model and neutrino emission model simultaneously with the HAWC gamma-ray data and IceCube neutrino data.We apply the method to search for galactic PeVatrons. Galactic PeVatrons are sources of PeV galactic cosmic rays. When the cosmic ray interacts with nearby material, it produces both gamma and neutrinos with a fixed relation between gamma-ray and neutrinos. We first perform a search for neutrino emissions from the 12 known gamma-ray sources detected by LHAASO.  A more detailed multimessenger search on Galactic PeVatrons candidates using the HAWC gamma-ray data and IceCube neutrino data is then conducted. We model the gamma-ray emission using the HAWC data and jointly fit a unified model on the gamma-ray and neutrino data. No significant detection was found and we can put constraints on the fraction of the gamma rays due to hadronic interactions.

Standard Model is an amazing success of particle physics, a success further cemented by the discovery of the Higgs boson. While its picture is incredibly satisfying, there are still a few mysteries it cannot address, one of which is the nature of dark matter.

While we have overwhelming evidence for its existence, we still do not know its basic properties such as mass or spin. Ultralight fields are among the most exciting dark matter candidates. Their large occupation number allows us to treat them as classical fields, while their non-relativistic velocities ensure that the field oscillates at an angular frequency equal to its mass with a long coherence time.

In this dissertation, we discuss some challenges associated with constructing successful models of ultralight dark matter and discuss new detection strategies.

In the first part of this dissertation, we address the underlying issue with ultralight scalars, namely the naturalness problem. Generally, requiring the scalar to couple to the Standard Model introduces radiative corrections to its mass, which conflicts with the requirement of a small mass. We present an ultraviolet-complete model that avoids this issue by employing $Z_N$ symmetry, which suppresses corrections to the mass while retaining relatively large couplings, making the model testable by current and future experiments.

In the second part of this dissertation, we focus on the experimental aspects of ultralight scalars. The general experimental landscape is divided into two categories: experiments assuming a dark matter background, and experiments measuring the fifth force associated with the new scalar.

The former provides strong constraints for the lightest scalars due to their large abundance, while the latter provides more conservative but robust limits on scalar interactions across many decades in scalar mass. We propose a novel approach based on measuring scalar potential using atomic and nuclear clocks, which complements fifth force measurements and offers significant improvements over current bounds.

In the third part of the dissertation, we shift our attention to vector dark matter. Specifically, we consider a scenario where some of the lepton generations are charged under a new gauge field. In this case, neutrino decays in the early universe impose strong constraints on their couplings, particularly for the lightest vectors. At higher masses, neutrino oscillations become a leading constraint due to the sourcing of the field by electrons affecting their oscillations. We demonstrate that in the presence of vector dark matter, the influence of the background field on neutrinos is even more pronounced, significantly enhancing constraints on the lightest vectors by several orders of magnitude.

Advancements in our understanding of new physics can be largely divided into two areas of study:  phenomenology and theory with the former concerning the formulation of new theories and holding them to scrutiny against experimental evidence while the latter involves the in-depth study of these theories to better understand the scope of their implications. To reflect this dichotomy, this thesis is broken into two acts: one covering progress made on the phenomenological front and the other covering progress made on the theoretical front. This defense will focus on the latter by detailing advancements made in our understanding of the structure of magnetic monopoles. In the mid-1970's, t'Hooft and Polyakov discovered magnetic monopoles exist as generic solutions in spontaneously broken gauge theories. Since then much progress has been made in understanding these monopoles, most notably by Callan who argued that the fermion vacuum is non-trivial around a magnetic monopole and can be interpreted as bound states of fermions with fractional fermion number. In this work, we explicitly compute these fermion bound states in an SU(2) gauge theory coupled to N_f  fermions. We demonstrate there are two unique ways to grant mass to the fermions in the SU(2) theory which, after symmetry breaking, both give a theory of QED with N_f massive fermions. Despite this seeming equivalence of the two theories at low energies, we demonstrate that the structure of the fermion bound states differ drastically between them and as a consequence can encode information about the high-energy theory, which is accessible at low-energy scales. We find that each theory exhibits a different number of stable excited dyonic states of the monopole with differing charges and energies. We find the ground states can also differ in energy and charge between the two theories. We demonstrate the monopole can inherit a mass correction and charge distribution that depends on the topological  angle even if one of the fermions is massless. This effect is present in one of the theories and is completely absent in the other. Finally, we discuss the implications of these effects on the SU(5) GUT monopole.

This dissertation is based on two independent projects.

Ultracold atoms trapped in optical lattices have proven to be a versatile, highly controllable, and pristine platform for studying quantum many-body physics. However, the characteristic single-particle energy scale in these systems is set by the recoil energy E_R = h²/ (8md²). Here, m is the mass of the atom, and d, the spatial period of the optical lattice, is limited by diffraction to λ/2, where λ is the wavelength of light used to create the optical lattice. Although the temperatures in these systems can be exceedingly low, the energy scales relevant for investigating many-body physics phenomena, such as superexchange or magnetic dipole interactions, can be lower yet. This limitation can be overcome by raising the relevant energy scales of the system (E_R^eff = h²/ (8md_eff²)) by engineering optical lattices with spatial periodicities below the diffraction limit (d_eff < λ/2).

To realize this subwavelength-spaced lattice, we first generated a Kronig-Penney-like optical lattice using the nonlinear optical response of three-level atoms in spatially varying dark states. This conservative Kronig-Penney-like optical potential has strongly subwavelength barriers that can be less than 10 nm (≡ λ/50) wide and are spaced λ/2 apart, where λ is the wavelength of light used to generate the optical lattice. Using the same nonlinear optical response, we developed a microscopy technique that allowed the probability density of atoms in optical lattices to be measured with a subwavelength resolution of λ/50. We theoretically investigated the feasibility of stroboscopically pulsing spatially shifted 1D Kronig-Penney-like optical lattices to create lattices with subwavelength spacings. We applied the lattice pulsing techniques developed in this theoretical investigation to realize a λ/4-spaced optical lattice. We used the subwavelength resolution microscopy technique to confirm the existence of this λ/4-spaced optical lattice by measuring the probability density of the atoms in the ground band of the λ/4-spaced optical lattice.

Single neutral atoms trapped in optical tweezer arrays with Rydberg interaction-mediated entangling gate operations have recently emerged as a promising platform for quantum computation and quantum simulation. These systems were first realized using atoms of a single species, with alkali atoms being the first to be trapped in optical tweezers, followed by alkaline-earth (like) atoms, and magnetic lanthanides. Recently, dual-species (alkali-alkali) optical tweezer arrays were also realized. Dual-species Rydberg arrays are a promising candidate for large-scale quantum computation due to their capability for multi-qubit gate operations and crosstalk-free measurements for mid-circuit readouts. However, a dual-species optical tweezer array of an alkali atom and an alkaline-earth (like) atom, which combines the beneficial properties of both types of atoms, has yet to be realized. In this half of the thesis, I present details on the design and construction of an apparatus for dual-species Rydberg tweezer arrays of Rb (alkali) and Yb (alkaline-earth like).

Understanding the dynamics of non-equilibrium quantum systems has long been a challenge across a wide range of physical phenomena. Recent advancements in various quantum technologies have propelled theoretical investigations of non-equilibrium quantum many-body dynamics. A key part of the theory is the development of computational methods, leading to significant results and a promising direction for further development. Nevertheless, simulating these complex systems using classical algorithms remains notoriously difficult, primarily due to the challenge of identifying physically principled and efficient approximations capable of reducing their computational complexity.

This thesis presents a collection of theoretical and numerical studies focusing on non-equilibrium dynamics of quantum many-body systems, with a particular emphasis on the steady-state transport of conserved quantities in various one-dimensional spin systems. In these systems, transport phenomena can be effectively captured by utilizing boundary-driven open quantum setups. Our investigations focus on various aspects of the non-equilibrium dynamics induced by novel boundary-driven systems. The aim is to comprehend a range of steady-state phenomena and to push the boundaries of simulation capacity using current state-of-the-art technologies.

In the first part, we delve into the non-equilibrium steady-state (NESS) phases of an interacting Aubry-André-Harper model, where a quasiperiodic potential gives rise to intriguing emergent collective phenomena. The peculiar spin transport and quantum correlation structure observed suggest the existence of multiple dynamical phases lying between the extensively studied thermal and many-body-localized phases.

Moving on to the second part, we explore the impact of operator weight dissipation on the scaling behavior of transport in various spin models. Our findings indicate that the effect of dissipation on transport is influenced by its impact on the system's conserved quantities. When dissipation preserves these symmetries, it maintains the scaling of the system's transport properties; however, when it breaks these conserved quantities, it leads the system towards diffusive scaling of transport.

In the third part, we investigate energy transport within the non-integrable regime of the Z3 chiral clock model, employing Lindblad operators with adjustable size and temperature. Through scaling analysis, we extract the transport coefficients of the model at relatively high temperatures, both above its gapless and gapped low-temperature phases. Furthermore, we calculate the temperature dependence of the energy diffusion constant across various model parameters, including the regime where the model exhibits quantum critical behavior at low temperatures.

Quantum simulation is perhaps the most natural application of a quantum computer, where a precisely controllable quantum system is designed to emulate a more complex or less accessible quantum system. Significant research efforts over the last decade have advanced quantum technology to the point where it can achieve `quantum advantage' over classical computers, enabling the exploration of complex phenomena in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. While the realization of a universal fault-tolerant quantum computer remains a future goal, analog quantum simulators--featuring continuous unitary evolutions with 50 to 100 qubits--have been developed across several experimental platforms. A key challenge in this field is balancing the control of these systems with the need to scale them up to address more complex problems. Trapped-ion platforms, with exceptionally high levels of control enabled by laser-cooled and electromagnetically confined ions, and all-to-all entangling capabilities through precise control over their collective motional modes, have emerged as a strong candidate for quantum simulation and provide a promising avenue for scaling up.

In this dissertation, I present my research work, emphasizing both the scalability and controllability aspects of a ¹⁷¹Yb⁺ based trapped-ion platform, with an underlying theme of analog quantum simulation. The initial part of my research involves utilizing a trapped ion apparatus operating within a cryogenic vacuum environment, suitable for scaling up to hundreds of ions. I address various challenges associated with this approach, particularly the impact of mechanical vibrations originating from the cryostat, which can induce phase errors during coherent operations. Subsequently, I detail the implementation of a scheme to generate phase-stable spin-spin interactions that are robust to vibration noise.

In the second part, using a trapped-ion quantum simulator operating at room temperature, we investigate the non-equilibrium dynamics of critical fluctuations following a quantum quench to the critical point. Employing systems with up to 50 spins, we show that the amplitude and timescale of post-quench fluctuations scale with system size, exhibiting distinct universal critical exponents. While a generic quench can lead to thermal critical behavior, a second quench from one critical state to another (i.e., double quench) results in unique critical behavior not seen in equilibrium. Our results highlight the potential of quantum simulators to explore universal scaling beyond the equilibrium paradigm.

In the final part of the thesis, we investigate an analog of the paradigmatic string-breaking phenomena of Quantum Chromodynamics using a quantum spin simulator. For this purpose, we employ an integrated trapped ion apparatus with 13 spins. This setup utilizes the individual controllability of laser beams to program a uniform spin-spin interaction profile across the chain, alongside 3D control of the local magnetic fields. We introduce two static probe charges, realized through local longitudinal magnetic fields, that create string tension. By implementing quantum quenches across the string-breaking point, we elucidate the patterns of dynamical string breaking, monitoring non-equilibrium charge evolution with spatio-temporal resolution. Furthermore, by initializing the charges away from the string boundary, we generate isolated charges and observe localization effects that arise from the interplay between confinement and lattice effects.

Quantum simulation stands as an important application of quantum computing, offering insights into quantum many-body systems that are beyond the reach of classical computational methods. For many quantum simulation applications, accurate initial state preparation is typically the first step for subsequent computational processes. This dissertation specifically focuses on state preparation procedures for quantum states with chiral topological order, states that are notable for their robust edge modes and topological properties. These states are interesting due to their profound connections to the behavior of electrons and spins in real-world solid-state materials. In this dissertation, we explore a type of state preparation procedure known as entanglement renormalization circuits. This class of quantum circuits is characterized by its hierarchical arrangement of quantum gates (or quantum operations in general), which systematically organize and prepare the entanglement of the target states across various length scales.

In the first part of the dissertation, we present an entanglement renormalization circuit for a non-interacting chiral topological system. The non-interacting chiral topological system we consider is a continuous Chern insulator model, which can serve as a toy model for the integer quantum Hall effect. The entanglement renormalization circuit for the continuous Chern insulator is the continuous multiscale entanglement renormalization ansatz (cMERA). The cMERA circuit, adapted for field theories, provides a natural framework for quantum systems that are continuous in momentum space. One of the key findings of this work is that we find a scale-invariant cMERA for which the continuous Chern insulator is a fixed-point wavefunction, a property that is believed to be impossible within the traditional lattice multiscale entanglement renormalization ansatz (MERA) framework. Furthermore, we provide an experimental proposal to realize the cMERA circuit using cold atoms.

In the second part of this dissertation, we shift our focus to entanglement renormalization circuits for interacting chiral topologically ordered states. We analytically derive a class of exactly solvable chiral spin liquids, classified under Kitaev's 16-fold way. Some of these chiral spin liquids share universal properties with certain fractional quantum Hall states. We then construct entanglement renormalization circuits for these chiral spin liquids by combining traditional MERA circuits with time-dependent quasi-local Hamiltonians. We refer to this class of circuits as the multiscale entanglement renormalization ansatz with quasi-local evolution (MERAQLE).

One of the central problems in many-body physics, both classical and quantum, is the relations between different notions of chaos. Ergodicity, mixing, operator growth, the eigenstate thermalization hypothesis, and spectral chaos are defined in terms of completely different objects in different contexts, don't necessarily co-occur, but still seem to be manifestations of closely related phenomena.

In this dissertation, we study the relation between two notions of chaos: thermalization and spectral chaos. We define a quantity called the Total Return Probability (TRP) which measures how a system forgets its initial state after time $T$, and show that it is closely connected to the Spectral Form Factor (SFF), a measure of chaos deriving from the energy level spectrum of a quantum system.

The main thrust of this work concerns hydrodynamic systems- systems where locality prevents charge or energy from spreading quickly, this putting a throttle on thermalization. We show that the detailed spacings of energy levels closely capture the dynamics of these locally conserved charges.

We also study spin glasses, a phase of matter where the obstacle to thermalization comes not from locality but from the presence of too many neighbors. Changing one region requires changing nearby regions which requires changing nearby-to-nearby regions, until only catastrophic realignments of the whole system can fully explore phase space. In spin glasses we find our clearest analytic link between thermalization and spectral statistics. We analytically calculate the spectral form factor in the limit of large system size and show it is equal to the TRP.

Finally, in the conclusion, we discuss some ideas for the future of both the SFF and the TRP.

The ergodic theory of classical dynamical systems, originating in Boltzmann's ergodic hypothesis, provides an idealized description of how the flow of information within energy surfaces of a classical phase space justifies the use of equilibrium statistical mechanics. While it is an extremely successful mathematical theory that establishes rigorous foundations for classical chaos and thermalization, its basic assumptions do not directly generalize to quantum mechanics. Consequently, previous approaches to quantum ergodicity have generally been limited to model-specific studies of thermalization, or well-motivated but imprecise general conjectures.

In this Dissertation, we develop a general theoretical framework for understanding how the energy levels of a quantum system drive the flow of quantum information and constrain the applicability of statistical mechanics, guided by two prominent conjectures. The first of these, the Quantum Chaos Conjecture (QCC), aims to characterize which quantum systems may thermalize, by postulating a connection between ergodicity or chaos and the statistical properties of random matrices. The second, the Fast Scrambling Conjecture (FSC), is concerned with how fast a quantum system may thermalize, and posits a maximum speed of thermalization in a sufficiently “local” many-body system.

This Dissertation is divided into three main parts. In the first part, Theory of Quantum Dynamics and the Energy Spectrum, we tackle these conjectures for a general isolated quantum system through results that may be understood as new formulations of the energy-time uncertainty principle. For QCC, we introduce precise quantum dynamical concepts of ergodicity and quantitatively establish their connections to the statistics of energy levels, deriving random matrix statistics as a special consequence of these dynamical notions. We subsequently build on one of these connections to derive an energy-time uncertainty principle that accounts for the full structure of the spectrum, introducing sufficient sensitivity for many-body systems. The resulting quantum speed limit allows us to prove a precise formulation of FSC from the mathematical properties of the energy spectrum. In doing so, we generalize QCC beyond the statistics of random matrices alone, and FSC beyond requirements of locality, establishing precise versions of these statements for the most general quantum mechanical Hamiltonian.

In the second part, Quantum Systems Beyond the Chaotic-Integrable Dichotomy, we demonstrate the need for the aforementioned precise formulations of these conjectures, by showing that looser formulations can be readily violated in “maximally” chaotic or integrable systems that would be most expected to satisfy them. Finally, in the third part, Experimental Probes of Many-Body Quantum Ergodicity, we develop tools to experimentally probe the structure of energy levels associated with ergodic dynamics, and demonstrate a generalization of these probes to open systems in an experiment with trapped ions.

Quantum information science offers a remarkable promise: by thinking practically about how quantum systems can be put to work to solve computational and information processing tasks, we gain novel insights into the foundations of quantum theory and computer science. Or, conversely, by (re)considering the fundamental physical building blocks of computers and sensors, we enable new technologies, with major impacts for computational and experimental physics.

In this dissertation, we explore these ideas through the lens of three different types of quantum hardware, each with a particular application primarily in mind: (1) networks of quantum sensors for measuring global properties of local field(s); (2) analog quantum computers for solving combinatorial optimization problems; and (3) digital quantum computers for simulating lattice (gauge) theories.

For the setting of quantum sensor networks, we derive the fundamental performance limits for the sensing task of measuring global properties of local field(s) in a variety of physical settings (qubit sensors, Mach-Zehnder interferometers, quadrature displacements) and present explicit protocols that achieve these limits. In the process, we reveal the geometric structure of the fundamental bounds and the associated algebraic structure of the corresponding protocols. We also find limits on the resources (e.g. entanglement or number of control operations) required by such protocols.

For analog quantum computers, we focus on the possible origins of quantum advantage for solving combinatorial optimization problems with an emphasis on investigating the power of adiabatic quantum computation with so-called stoquastic Hamiltonians. Such Hamiltonians do not exhibit a sign problem when classically simulated via quantum Monte Carlo algorithms, suggesting deep connections between the sign problem, the locality of interactions, and the origins of quantum advantage. We explore these connections in detail.

Finally, for digital quantum computers, we consider the optimization of two tasks relevant for simulating lattice (gauge) theories. First, we investigate how to map fermionic systems to qubit systems in a hardware-aware manner that consequently enables an improved parallelization of Trotter-based time evolution algorithms on the qubitized Hamiltonian. Second, we investigate how to take advantage of known symmetries in lattice gauge theories to construct more efficient randomized measurement protocols for extracting purities and entanglement entropies from simulated states. We demonstrate how these protocols can be used to detect a phase transition between a trivial and a topologically ordered phase in $Z_2$ lattice gauge theory. Detecting this transition via these randomized methods would not otherwise be possible without relearning the symmetries.

Chirality, the property of objects possessing non-superimposable mirror images, initially identified and explored in organic and biological molecules, has gained growing interests in the realm of inorganic nanomaterials due to its foreseeable applications in the fields such as Enantiochemistry, Nanophotonics, Spintronics.

In the first segment of this dissertation, we demonstrate a bottom-up synthetic strategy to induce chirality in plasmonic nanoparticles and hybrid plasmonic-semiconductor nanostructures. Subsequently, we detail a simplified analytical coupled-oscillators model to facilitate the understanding of plasmonic-chiral coupling and predict various chiroptical responses based on different coupling strengths, validated through finite element method simulations. Furthermore, advancements in characterizing nanoscale chirality with high spatial resolution at the single nanoparticle level are explored using a novel polarization-dependent optical atomic force microscopy technique, overcoming resolution limits in far field measurements. Finally, we demonstrate the employment of nanoscale chirality to induce spin polarization and enable unique nanoscale chiral Floquet engineering.