PhD Defenses 2025

This thesis investigates the magnetotransport and magnetic properties of the correlated insulator FeSb₂ and its doped derivatives, motivated by reports of metallic surface states, emergent surface magnetism, and theoretical predictions of unconventional magnetism in substituted FeSb₂. The thesis is organized into three major components: (1) the surface magnetotransport properties of FeSb₂, (2) the surface magnetic properties of FeSb₂, and (3) the magnetic and magnetotransport behavior arising from Cr-, Co-, and Te-doping. In this defense, I will focus on the first two components, which address the nature of the FeSb₂ surface. Using a Corbino disk geometry to isolate individual crystal facets, I show that the low-temperature surface conduction channel is a thin but three-dimensional metallic layer exhibiting anisotropic magnetoresistance consistent with magnetocrystalline anisotropy tied to a [100] easy axis. Complementary magnetic susceptibility measurements reveal a distinct Curie–Weiss–like surface magnetic contribution with anisotropy matching that seen in transport, and an anomalous Hall component further evidencing magnetic correlations in the surface conduction path. Together, these results constitute the first demonstration of surface magnetism in FeSb₂ and establish that its surface hosts an anisotropic, metallic, and magnetically correlated state despite the absence of bulk magnetism.

This thesis explores silicon as a platform for dopant-based quantum computation and analog quantum simulation, employing scanning tunneling microscope (STM) lithography to achieve atomically precise device structures. Beginning with a comprehensive review of the device fabrication process and a theoretical introduction to transport in dopant-based nanostructures, this thesis establishes a framework for constructing dopant-based devices where both spin and charge degrees of freedom can be harnessed for quantum information processing. To address the challenge of scalability, automated STM patterning workflows are developed. Algorithms inspired by electronic design automation (EDA) are introduced to accelerate the creation of both atomically precise quantum structures and large-area electrical leads.

The experimental chapters present device architectures for spin readout and analog quantum simulation. Charge sensing and energy-selective spin readout are demonstrated using a donor-dot single electron transistor (SET). Spin relaxation times (T₁) are measured across varying magnetic fields showing relaxation occurs mainly through charge noise enhanced spin-orbital coupling. These results provide a foundation for implementing spin manipulation in the next stage of development. Works on analog quantum simulation include the experimental realization of the two-dimensional Hubbard model using dopant arrays, supported by numerical simulations based on an extended Fermi-Hubbard model. Spin filling in these arrays is further investigated through magnetotransport measurements, revealing a “Hund’s rule” like behavior in electron configurations. In addition, a 32×32 quantum dot array was fabricated to extend the study beyond small systems, enabling the simulation of transport through localized electronic states and the exploration of disorder-induced conduction phenomena.

Finally, I present results on optimized RF reflectometry circuits for charge sensing in a donor-dot SET, achieving a minimum integration time of 600 ns to resolve charge states on a donor cluster. Applied to a 3×3 quantum dot array, these techniques identify site-resolved charge addition lines through distinct capacitive couplings to the leads, enabling unambiguous assignment of electron occupation across the lattice. These studies demonstrate the versatility of atomically precise dopant systems in probing strongly correlated electron physics and advancing silicon-based quantum information processing.

Learning states and noise is a crucial part of quantum computation, whether it is to verify state preparation, benchmark gates, or learn the outcome of a quantum circuit. This thesis falls under this broad theme and is divided into the following two parts.

The first part of the thesis focuses on quantum state tomography of continuous-variable states and obtaining precision bounds using shadow tomography. Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called `classical shadows', with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical shadow framework, obtaining rigorous bounds on the number of independent measurements needed to estimate density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols using our method, and benchmark these results against numerical simulations as well as experimental data from optical homodyne experiments.

The second part focuses on open quantum systems with non-Markovian, or time-correlated, interactions. We studied them through the output of a popular benchmarking technique called Randomized Benchmarking. Our work shows how non-Markovianity in system-environment interactions impacts the RB output of the system. To show this we introduced two models that exemplify Markovian and non-Markovian interactions, created an efficient algorithm to study the latter nontrivial model, and examined the outputs. We observed a non-exponential decay of average sequence fidelity in the non-Markovian model that fits a power-law times exponential decay, which is a marked distinction from a Markovian model. We also place our framework on a firm mathematical basis and verify our models through established methods of identifying non-Markovianity in quantum systems.

Finally, we designed a compressive tomography approach for learning non-Markovian quantum dynamics. Our method employs machine learning to RB data to reconstruct system-environment interaction unitaries from experimentally accessible fidelity decay. By only operating on the accessible levels of the system, we demonstrate successful characterization of complex quantum dynamics involving both coherent and incoherent environments simultaneously. The approach leverages gradient optimization with SU(n) parameterization to learn the complete interaction unitary, guided by RB fidelities. We applied this framework to realistic exchange-only qubit models to successfully quantify leakage transitions between computational and charge states, achieving very high reconstruction fidelities. The learned models demonstrate robust extrapolation beyond training regimes, accurately predicting system behavior for sequence lengths up to five times longer than training data. These results inform efforts to incorporate non-Markovian quantum noise in the characterization and benchmarking of quantum devices.

Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. In this dissertation, I describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully-controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to  reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.

 I also advance this method in two complementary directions: expanding its applicability to a larger class of noise spectra, and simplifying its implementation. First, we extend the random pulse sequences method to reconstruct piecewise-linear noise spectra, which more realistically model many physical systems. We show through numerical simulations that the new method resolves finer spectral features while maintaining an order-of-magnitude speedup over conventional approaches to noise spectroscopy. Second, we introduce a simplified variant using Rademacher measurements, optimized for sparse spectra, that greatly reduces experimental complexity without compromising reconstruction accuracy. Together, these developments broaden the reach of random pulse sequences noise spectroscopy and enhance its practicality for high-resolution, resource-efficient noise characterization in realistic quantum systems.

The RSA (Rivest–Shamir–Adleman) encryption is believed to be secure because there is no known classical algorithm that can calculate the prime factors of a number in polynomial time. Shor's algorithm can, in principle, solve this problem in polynomial time on a scalable quantum computer. Shor's algorithm is an application of quantum phase estimation where one factorizes a number by finding the periodicity of the modular multiplication operator. Quantum modular multiplication is related to the classically chaotic baker’s map. However, modular multiplication itself is periodic. It raises the question: Is there any signature of chaos in modular multiplication? In this dissertation, we show that the answer is yes. We prove that modular multiplication is a linear combination of chaotic quantized baker’s maps. The periodicity of modular multiplication arises from ‘destructive interference’ of chaotic maps. Building on this result, we design a quantum circuit for modular multiplication that is based entirely on the discrete Fourier transform and its variants. In the final part of this dissertation, we study the integrability of the discrete Gross-Neveu model. We show that the action of the discrete Gross-Neveu model has a saddle point corresponding to soliton solutions. We further explore the connection between solitons and reflectionless potential using tools from discrete supersymmetry.

Despite the remarkable success of artificial intelligence (AI), we still lack a fundamental understanding of why deep learning works—why certain architectural designs are preferred, how optimization navigates complex landscapes, and what data characteristics enable learning. This dissertation addresses these questions through a phenomenological approach, abstracting essential features from complex real-world experiments and constructing minimal setups that faithfully capture them. The investigation unfolds in three interconnected parts.

In the first part, we study signal propagation in randomly initialized networks under the infinite-width limit, revealing a phase transition from ordered to chaotic dynamics at large depth. We introduce the inter-layer Jacobian as an observable that precisely characterizes this transition. Through extensive empirical validation, we demonstrate that this metric provides universal guidance and an efficient algorithm for selecting network initializations across diverse architectures, offering a principled alternative to heuristic initialization schemes.

In the second part, we elucidate the optimization landscape of neural networks by carefully analyzing the dynamics of the loss Hessian (sharpness) under gradient descent. Remarkably, we show that even a minimal two-layer linear network trained on a single example exhibits all the essential sharpness phenomenology observed in real-world scenarios. By analyzing the structure of dynamical fixed points in function space, we reveal the fundamental mechanisms governing sharpness evolution during training, thereby clarifying the interplay between initialization, parameterization, and gradient descent dynamics at large learning rates.

In the third part, we investigate how data characteristics and network architecture choices give rise to the emergent capabilities of neural networks. We begin by analyzing models trained on modular arithmetic tasks. Across different setups, we establish necessary data-diversity thresholds and minimal network sizes for successful task performance, demonstrating that certain computational capabilities emerge only when both architectural capacity and data coverage exceed critical values. Furthermore, we extend this understanding to a more practical setting by tackling pseudo-random number generator (PRNG) tasks.

Finally, synthesizing insights from the preceding parts, we challenge conventional architectural design paradigms. We propose a new (proto-)architecture that enables arbitrary, learned inter-layer connectivity patterns. Through careful analysis of trained models in both vision and language domains, we observe the emergence of distinct connectivity structures, accompanied by interpretable layer specialization and meaningful correlations between the nature of the data and the network’s internal computational patterns.

This dissertation consists of three research projects which deal with laser-matter interactions and potential applications of the processes.

In the first part of this dissertation, I present, analyze, and simulate a mechanism for remotely generating RF radiation in air by using a laser pulse train (LPT). The LPT ionizes the air through photo and collisional ionization, generating a plasma filament. The ponderomotive forces of the LPT drive radial and longitudinal plasma currents. These plasma currents generate radiation at the LPT repetition rate, which can be tuned in the 0.5 – 6.0 GHz range. Of particular interest is the RF generation in the 1.4-1.7 GHz regime. This is the operating frequency range of all GPS signals. The analysis and simulation results of the RF radiation are shown to be in agreement with experimental data. The experiments were performed in collaboration with the theory and computational work at the University of Maryland.

The second part of this dissertation analyzes and simulates long range propagation and stability of laser pulses traveling vertically through the turbulent atmosphere. By tailoring the initial pulse parameters, the pulse can be focused transversely and longitudinally at remote locations (>50 km) with intensity enhancements of > 10³. The potential application of this research is on the long-range generation of RF signals in a turbulent atmosphere. Nonlinear self-focusing of the laser pulse and dispersion lead to the growth of a hybrid modulation-filamentation instability, which causes both transverse and longitudinal beam breakup. This hybrid instability is analyzed and numerically simulated for pulses propagating in the atmosphere.

The third part of this dissertation presents a mechanism for generating tunable low frequency radiation in the ionosphere and propagating the low frequency signal back to the ground. This process has the potential to be used as a new type of over-the-horizon (OTH) radar which would be compact, mobile, and far less costly than conventional OTH systems. Conventional OTH radar systems utilize dipole antenna arrays that span multiple kilometers, and can cost well over a billion dollars. Most major countries employ conventional OTH radar systems. The proposed mechanism relies on a ground-based, modulated RF source. By tuning the modulation frequency to the local plasma frequency in the ionosphere (F layer), a current can be resonantly excited by the ponderomotive force of the modulated signal. This current grows in time and generates a low frequency signal at the local plasma frequency, which is in the MHz range. The low frequency signal propagates back to the ground, far from the source, where it can be detected. We find that using available RF sources, i.e., gyrotrons, detectable low frequency intensities can be generated and detected on the ground. The minimum detectable frequency is ~10^-18 W/m², though the theoretical limit may be lower. This mechanism has the potential to detect OTH objects using a compact, mobile, and far less expensive system than presently exists.

Neutron stars are rich testbeds for nuclear physics in environments unable to be reproduced on Earth. A key open question is the form of the neutron star equation of state, which describes the compressibility and deformability of the neutron star bulk material. The equation of state is directly related to observables such as the neutron star mass--radius relationship and the strength of gravitational wave emission from rotating neutron stars, called pulsars. Another open question is the composition of neutron stars' companions, which could range from rocky planets to ultra-dense remnants of stellar cores. Two novel measurements that would constrain the equation of state and companion composition are enabled by MeV $\gamma$-ray observations and presented in this dissertation. The first is a simulation of a pulsar's GeV $\gamma$-ray emission irradiating a range of companion types and re-emitting as 511 keV $\gamma$-rays, where the orbital dependence of the 511 keV $\gamma$-rays is directly related to companion composition. The second study searches for gravitational waves emitted by pulsars in 2 parts. The first part considers emission following the Vela pulsar glitch on April 29, 2024. The second part simulates possible joint gravitational wave searches with an MeV telescope and a gravitational wave antenna.AMEGO is a proposed MeV $\gamma$-ray observatory to address the need for new observations in this energy range. ComPair, a prototype of AMEGO, consists of four detector subsystems and completed a short duration high altitude balloon flight on August 27, 2023. This dissertation includes the development of the detector effects engine, a critical software package to accurately model the instrument, understand its response, and benchmark its performance. I also present the integration, test, and calibration of the ComPair anti-coincidence detector, and demonstrate that it rejects over 99\% of likely background charged particle events. This is followed by benchmarking the performance of the entire ComPair instrument during the balloon flight with Monte Carlo simulations. This analysis shows that ComPair met all of its goals, including rejecting the cosmic ray background, reconstructing Compton scattering and pair production $\gamma$-ray events, and measuring the $\gamma$-ray background. The dissertation concludes with a consideration of how the initial ComPair instrument's performance informs the design of ComPair's next generation.

This thesis presents developments in the theory and application of quantum learning. The first two chapters fall under the head of classical shadow tomography, a randomized measurement technique which estimates a large number of expectation values effectively in parallel. In the first chapter on this topic, we extend classical shadow state tomography to the characterization of quantum channels. We prove that with a simple protocol involving randomized measurement of randomly generated input states evolved through channel, one can estimate many channel properties in parallel, with rigorous guarantees on the sample complexity required. In the next chapter, we bring together finite-depth classical shadows, derandomization, and tensor network simulation to present an algorithm for tailoring a sequence of measurements to a set of observables of interest, demonstrating the effectiveness of our technique for a number of tasks in quantum chemistry and simulation. The second part of this thesis presents a step toward applying ideas from quantum learning to quantum error correction. We investigate the use of prior information on qubit error rates in the decoding task, showing that prior information can significantly change decoder performance when a small number of qubits have high error rates. We present a protocol to learn the location of error-prone sites from decoding data in real time, and then apply this in turn to develop in situ protocol for calibration of gates while processing logical information.

Spin glasses are, in essence, simply systems of magnetic moments with disordered interactions. Despite this basic premise, spin glasses have become relevant in a wide variety of fields, including condensed matter physics, complexity and optimization theory, error correction, quantum computing, machine learning, and even neuroscience. The pervasiveness of spin glasses stems from the fact that they are paradigmatic examples of how global complexity emerges from disordered interactions between a large number of basic constituents. The inclusion of quantum effects in spin glasses creates an even richer picture, due to the interplay between the energy barriers arising from disorder and quantum fluctuations which allow for tunneling.

This thesis initially focuses on quantum glasses and how their initial states explore their Hilbert spaces. Two complementary approaches are used. One is comparison of the spectral statistics, particularly the spectral form factor, with the spectral statistics of random matrix ensembles, a hallmark of quantum chaotic behavior. The other approach uses the Thouless-Anderson-Palmer mean-field equations to determine the number of local minima which appear in the free energy landscape.

This thesis then applies methods from spin glass theory to the field of machine learning. Neural networks, like spin glasses, are systems in which remarkable behavior emerges from interactions between basic constituents. By studying the phase diagrams of spin models analogous to snapshots of neural networks throughout their training process, insight is gained into the mechanisms of learning.

Finally, this thesis investigates how quantum effects can lead to advantages in machine learning. It is shown, through classical simulation and experiments on both trapped-ion and superconducting quantum computing hardware, that a natural quantization of a classical neural network can demonstrate superior generalization performance due to the injection of quantum uncertainty.

Advances in the coherent control of Rydberg atoms have led to an explosion in their use in a wide range of topics, including quantum computation, simulation, sensing, and networking. More specifically, Rydberg-coupled ensembles of atoms interfaced with a single mode of light have enabled studies of fundamental light-matter interactions at the single-photon level and have emerged as a promising platform to realize scalable quantum networking nodes.

In the first part of this thesis, we utilize Rydberg blockade to generate large ensembles that host a single Rydberg excitation and use the collective state as a resource to efficiently generate single photons. We further investigate the shelving of the collective Rydberg excitations to the ground-state manifold, where we observe an order of magnitude increase in the coherence time of the excitation.

In the latter half of the thesis, we use near-resonant microwave fields to generate microwave-dressed Rydberg states, where we utilize the degrees of freedom of the microwave field to tune the strength, form, and angular dependence of the dipole-dipole interactions. To this end, we develop a robust and highly tunable microwave polarization control system. We use a set of in-vacuum electrodes as microwave antennas. We measure the microwave polarizations produced by each source at the positions of the atoms using a Rydberg EIT-based polarimetry technique. By characterizing the three imperfect sources, we find the control settings necessary to produce s-, p, and s+ polarized microwaves with >99 % fidelity. We extend our purification techniques to frequencies away from Rydberg resonances by utilizing an auxiliary microwave field, generating two-photon microwave resonances.

The high-fidelity microwave polarizations are used to resonantly admix opposite-parity Rydberg states, generating dressed states with dipole-dipole interactions that are longer range and stronger than the bare van der Waals interactions. To characterize the strength of the interactions, we measure the photon-number statistics of the light generated by the ensemble of atoms. By varying the cloud length relative to the blockade radii, we demonstrate a clear enhancement of the interaction strength due to microwave dressing. Our platform enables further engineering of interactions by exploiting the polarization and frequency degrees of freedom of the microwave fields, opening pathways for new quantum control strategies in many different experimental platforms.

Quantum simulation is a powerful approach for studying complex quantum systems, as it utilizes the behavior of one system to model, and thereby understand, features of another--otherwise inaccessible--system. Ultracold atomic gases as quantum simulators have become a central platform for engineering analog quantum systems in experimentally accessible environments.  Here, localization physics were investigated in Rb-87 Bose-Einstein condensates subjected to artificial gauge fields and disorder over a range of energy and time scales, in both equilibrium and out-of-equilibrium settings. The simulated effective Hamiltonian was implemented by driving two-photon Raman transitions with laser fields, combined with tunable intensity patterns from a digital micromirror device (DMD) that generated disordered potential landscapes. By varying the experimental protocols—including the loading times of the Raman coupling and disorder, as well as the disorder strength—we obtained insight into how artificial gauge fields respond in the presence of disorder.  The resulting dynamics revealed rich behavior: including inhomogeneous global magnetization for high-energy dynamics and increases in the condensate width for pulsed disorder in lower energy and near-equilibrium conditions; lastly, signatures of localization, in the form of damped oscillations, were observed as the system was driven out-of-equilibrium.

Collective cell migration is essential in biological processes such as tissue formation, wound healing, cancer progression, and immune response. However, quantitatively linking collective behavior to cell identity, genetic background, and environmental context remains a challenge. This thesis presents a multiscale analysis framework that extracts and interprets motion phenotypes from both in vitro and in vivo systems, combining computational tools with biological insight.

We first developed an AI-based, label-free tracking method to analyze cell motion in epithelial monolayers using phase contrast images. From these tracks, we computed motion metrics such as D2min, which captures local non-affine rearrangements, and affine deformation, which reflects coordinated motion. Applying these metrics to a panel of breast epithelial and cancer cell lines, we found that more invasive cells display higher D2min and less directional affine motion. These metrics reliably distinguish non-tumorigenic, tumorigenic, and metastatic behaviors.

We then explored how physical cues like nano-ridged substrates affect migration. While topography enhanced speed and directionality, it had a limited effect on mixing. Instead, we found that cell identity, in our case, KRas and PTEN mutations, dominates the response, overriding environmental influence and maintaining segregation despite changes in substrate.

To extend this analysis to live tissues, we applied 3D optical flow to intravital imaging data of immune cells in mouse tumors. This approach captured collective myeloid motion near tumor lesions and revealed dynamic motion hotspots. We tracked these regions over time and observed that early-stage motion patterns may relate to whether lesions progress or regress, suggesting a potential predictive role for immune behavior.

Together, these studies demonstrate that collective cell motion is shaped by both internal genetic programs and external environments. This thesis provides a scalable and label-free framework for quantifying motion behavior across systems, offering tools for both basic biology and translational research.

Topological responses rooted in the Berry phase play an important role in modern condensed matter physics. However, in interacting quantum systems, the robustness and observability of such responses require careful analysis and examining. This dissertation comprises two studies on how topological phenomena, namely the chiral anomaly and the anomalous Hall effect, emerge and are (un)renormalized in interacting quantum systems.

The first part investigates the robustness of the chiral anomaly in interacting systems through a mixed anomaly framework. The chiral anomaly is one of the robust quantum effects in relativistic field theories with chiral symmetry, where charges in the chiral sectors appear to be separately conserved. The chiral anomaly, which is often associated with a renormalization-invariant topological term, is a violation of this conservation law because of quantum effects. In condensed matter systems like Weyl semimetals, analogous phenomena emerge as charge pumping between Fermi pockets under electromagnetic fields. However, because the chiral charge is defined in terms of low energy quasiparticles, most studies of the chiral anomaly in condensed matter apply to effectively non-interacting systems. We apply an approach in which the chiral symmetry in solid materials is viewed as a so-called emanant symmetry of the underlying space translation symmetry, a mixed anomaly between the charge U(1) and space translation. In this framework, the chiral charge is associated with total momentum, and we show that the corresponding chiral anomaly remains unrenormalized by interactions in contrast to other chiral charges in (1+1)D whose renormalization is dependent on regularization. In (3+1)D, is equivalent to the charge transferred between Fermi surfaces which can be measured through changes in Fermi-surface-enclosed volume. To measure this effect, we propose a pump-probe technique.

The second part turns to another Berry-phase-related response, the anomalous Hall effect in the phase-disordered regime of chiral superconductors. Motivated by recent experiments showing evidence for chiral superconductivity in an anomalous Hall phase of tetralayer graphene, we study the relationship between the normal state anomalous Hall conductivity and that in the phase-disordered state slightly above the critical temperature of the superconductor. Numerical simulations show that the Berry phase on the Fermi surface determines the charge asymmetry between vortices and antivortices, resulting in a nonzero Hall response that is close to the normal-state anomalous Hall response. However, using a gauge-invariant superconducting response framework, we find that while the vortex charge is screened by interactions, the screening charge, after a time delay, reappears in the longitudinal current. Thus, in this phase, the dc Hall conductivity aligns with the ac Hall conductance of the superconducting and normal phases, rather than with the screened vortex charge.

Data collected by the Compact Muon Solenoid experiment at the Large Hadron Collider, which collides protons at a center-of-mass energy close to 14 TeV, allows tests of the Standard Model of Particle Physics and searches for physics beyond the Standard Model. This thesis presents a search for a beyond-the-standard-model particle, the Soft Unclustered Energy Pattern (SUEP), and studies of radiation damage to plastic scintillators, used to produce signals in the CMS calorimeter system.

The effects of ionizing radiation on the light output and the optical properties of plastic scintillators are assessed for a variety of matrix materials, dopant concentrations, fluors, antioxidant concentrations, sample thicknesses, doses, and dose rates. Depending on the dose rate, the samples exhibit internal regions with different refractive indices separated by a visible boundary. Measurements of the boundary depth indicate compatibility with the expected oxygen penetration depth during irradiation. The refractive indices of the internal regions are higher than those of the outer regions, which match the indices of unirradiated samples.

Dark sectors with a large t'Hooft coupling can give rise to SUEPs, which are final states characterized by large charged particle multiplicities. A search for SUEPs producing muons in the final state is also presented. The expected 95% CL upper limits for the cross sections indicate that once unblinded, the search will be able to set upper limits about 3-4 orders of magnitude lower than the theory predictions.

Quantum emitters coupled to a nanophotonic waveguide have revolutionized quantum science and technology by enabling engineered light-matter interactions. In particular, a system of neutral atoms coupled to an optical nanofiber (ONF) offers a unique platform for quantum optics and quantum computation, as it integrates two well-established technologies: neutral atoms with high-fidelity control and optical fibers with low-loss light propagation. This thesis presents a study of the collective dynamics of Rb85 atoms coupled to an ONF, with a focus on the atomic spatial distribution.

We first present the collective dynamics of V-type multilevel quantum emitters, emphasizing the interaction between multiple excited states and multiple atoms mediated by a common electromagnetic (EM) field mode. Remarkably, we observe quantum beats even in the absence of an initial superposition in the excited states, which arises from vacuum-induced coupling between the excited levels. Although such second-order processes are typically weak, they can become observable through collective enhancement. We theoretically investigate these collective quantum beats in an extended system of V-type atoms coupled to a waveguide and identify a characteristic length scale that governs the interference in the multi-atom, multi-level emission.

Then, we describe our efforts to observe long-range interaction between macroscopically separated atomic clouds via an optical fiber. We develop a theoretical framework for modeling resonant scattering of an atomic ensemble placed in front of a mirror in the waveguide quantum electrodynamics (QED) setup. We identify the competition of two parameters that govern the scattering process: the drive strength and the strength of time-delayed feedback. Our intensity correlation measurement shows that an atomic cloud coupled to an ONF operates in the independent emission regime, where time-delayed feedback is negligible. This work highlights the need for an ordered atomic array with a lattice constant commensurate with the transition wavelength to collectively enhance cooperativity.

In the final chapter, we present a novel method for creating a tunable-spacing atomic array interfaced with an ONF using a set of binary phase transmission gratings. The optical setup and preliminary results on atom trapping within the lattice are described. Our approach opens the door to high-cooperativity neutral-atom-nanofiber interfaces, paving the way for advances in quantum optics and quantum technology.

While the Standard Model (SM) is the most precise theory ever discovered, it is known to be incomplete. The SM cannot account for the observed Dark Matter (DM) in the universe or that the neutrinos have masses. Furthermore, theoretical puzzles such as the matter-antimatter asymmetry and the Planck-weak hierarchy remain unexplained within the SM. These shortcomings have motivated extensive efforts to search for physics beyond the SM (BSM).

One promising class of BSM theories involves “Hidden Sectors”, which are new particles and interactions that are singlets under SM gauge symmetries. While minimal hidden sector scenarios have been widely studied, models with non-minimal field content and richer dynamics remain less explored. In the first part of this dissertation, we examine both minimal and non-minimal hidden sector models, addressing open questions regarding their discovery potential. We evaluate the sensitivity of future lepton colliders to vector portal models across a range of benchmark scenarios, and demonstrate how neutrino telescopes can probe non-minimal hidden sectors using two simplified models.

Precision measurements of SM observables, such as electroweak precision observables (EWPOs) and the anomalous magnetic moment of the muon (g − 2), offer a complementary approach to direct searches by probing virtual effects of new physics.

A crucial input to global EW fits is the top quark mass mt, which must be known with high precision to fully exploit the sensitivity of these observables. However, most current methods are limited by uncertainties in production modeling and jet energy calibration. Moreover, they may be sensitive to BSM effects which can introduce a bias in the measured mt. In the second part of this dissertation, we propose a new method for measuring mt that reduces both sources of systematic uncertainty and providing complementary systematics. If implemented, this approach could significantly enhance the precision of current and future measurements, helping to sharpen indirect probes of BSM physics.

Fluxonium qubit is a promising elementary building block for quantum information processing due to its long coherence time combined with a strong anharmonicity. In this thesis, we first introduce a novel fluxonium qubit operating at zero magnetic field with high coherence. We implement and characterize single-qubit gates with an average gate fidelity of 99.93%, extracted from randomized benchmarking. This qubit serves as a ready-to-use superconducting qubit that operates in the frequency range of conventional transmons and exhibits stronger anharmonicity.

Next, we implement a 60 ns direct CNOT gate on two inductively coupled fluxoniums, which behave almost exactly like a pair of transversely coupled spin-1/2 systems. Notably, the typically undesirable static ZZ term, arising from non-computational transitions, is nearly absent even in the presence of strong qubit-qubit hybridization. The CNOT gate fidelity, estimated via randomized benchmarking, reaches 99.94%. Furthermore, this fidelity remains above 99.9% over a span of 24 days without any recalibration between measurements. Compared with the 99.96% fidelity of a 60 ns identity gate, our results constrain non-decoherence-related errors during logical operations to as low as . This work adds a simple and robust two-qubit gate to the still relatively small family of “beyond three nines” gates on superconducting qubits.

Quantum sensing faces challenges in moving from proof-of-concept demonstrations to practical technologies, with discrepancies between idealized theoretical frameworks and experimental realities presenting a key obstacle. This dissertation explores these nuances — with a focus on nitrogen-vacancy (NV) centers in diamond — through four projects spanning experiment, theory, simulations, and algorithmic optimization.

We characterize Ramsey envelope modulation effects in ¹⁵NV diamond magnetometry, showing that magnetic field misalignments produce envelope effects that degrade sensitivity. Next, we study the breakdown of Average Hamiltonian Theory (AHT) in experimental regimes, introduce exact methods to calculate a sensor response to a target signal that are valid beyond AHT, and establish symmetries that guarantee AHT convergence. With Ensemble Cluster Sampling (ECS), we address overfitting in quantum control by training algorithms on heterogeneous parameter distributions rather than idealized systems. Finally, we present TEMPO, an open-source Python package for accessible pulse sequence simulations.

These studies underline the need for continued collaboration between quantum sensing theory and laboratory applications, while maintaining an eye on modern algorithms and software.

Locality constrains the flow of information between different parts of many-body quantum systems. In quantum computers, this affects the ability to perform arbitrary interactions for quantum information processing tasks. A crucial challenge for scalable quantum architectures is thus to minimize the overheads due to locality constraints. Additionally, locality constraints affect the way information and entanglement can be spread in many body quantum systems, and our ability to make predictions about such systems.

One way to implement arbitrary interactions in locality-constrained architectures is by permuting qubits, also known as performing quantum routing. In the first part of this thesis, we investigate quantum routing strategies using emerging architectural capabilities beyond swap gates. We first investigate the use of mid-circuit measurements and classical feedback, which enable quantum teleportation. We prove upper bounds on the speedup afforded by the use of quantum teleportation for routing. We also design architectural connectivities which can exploit teleportation-based speedups. We then consider quantum routing by continuous-time Hamiltonian evolution, designing a routing algorithm that achieves a polynomial speedup in routing time over gate-based routing methods in architectures with a bottleneck, which is an intermediate region that constrains interactions between the rest of the device. We improve the lower bound on the time taken for routing in such systems, and develop a matching upper bound on the closely related task of generating and distributing entanglement.

 In the second part of this thesis, we investigate the behavior of finite-sized systems evolving by local Hamiltonians for a long duration. A major direction of research in condensed matter physics is the investigation of whether isolated systems thermalize (i.e., reach a state of thermal equilibrium). Various theoretical proposals such as information scrambling, entanglement between subsystems, and the eigenstate thermalization hypothesis have attempted to explain the conditions under which systems equilibrate. At the same time, notable counter-examples to thermalization have been found, such as systems that are integrable, exhibit many-body localization, or quantum many-body scars. We approach this question from a complexity-theoretic perspective. We show that the problem of deciding whether or not observables equilibrate to a given value is PSPACE-complete. We also show that deciding whether observables relax to the thermal equilibrium value is contained in PSPACE, and is PSPACE-hard under quantum polynomial time reductions. These problems are thus intractable even for a quantum computer. Our results indicate that the proposed conditions leading to thermalization are either difficult to decide, or are not generic indicators of thermalization. 

The interaction of intense lasers with plasma has opened the door to a plethora of new phenomena and applications including filamentation, high harmonic generation, and laser wakefield acceleration (LWFA). Fundamental to intense laser-matter interactions is nonlinear self-focusing, which can be exploited to achieve high peak intensities over longer interaction lengths than is possible with linear propagation.

In this dissertation, we study the propagation of intense self-focusing laser pulses in plasma. We demonstrate the ability to accelerate electron bunches up to 15 MeV via LWFA using few-cycle, mJ-scale pulses at a kHz repetition rate by taking advantage of relativistic self-focusing in near-critical density hydrogen plasma. Furthermore, we investigate the emergence of spatio-temporal optical vortices (STOVs)—electromagnetic structures with transverse orbital angular momentum (tOAM)—that arise in relativistic and non-relativistic filamentation. We find that these vortices are fundamental emergent features of such propagation and mediate the intrapulse flow of energy during filamentation. Lastly, we perform a simulation study of the linear and nonlinear propagation of STOV pulses in a simple plasma slab to elucidate the distribution of tOAM between particles and electromagnetic fields. We show that the particle-based tOAM is embodied by a polariton-like structure, as predicted in our group’s previous analytic theory.

The iron-based superconductor FeTeSe has emerged as a promising platform for combining superconductivity and topology for the realization of topological quantum computing. Additionally, the unconventional S+/- pairing symmetry has been shown to give rise to higher-order topological surface states in FeTeSe. Despite the interest in superconducting devices based on FeTeSe, there have been relatively few demonstrations of Josephson junctions in FeTeSe-based systems.

In this dissertation presentation, we will begin by providing an overview of the iron-based superconductor FeTeSe. Next, we will describe the Josephson effects observed in a FeTe0.55Se0.45-based device. We will highlight three deviations from the typical Josephson effects: 1) the existence of two distinct Josephson diffraction patterns under applied RF irradiation; 2) sudden ‘jumps’ in the diffraction pattern as RF power increases; and 3) a minimum critical current at zero magnetic field when RF irradiation is present. Finally, we will discuss some potential phenomena that could be responsible for the unusual Josephson effects measured in this FeTe0.55Se0.45-based device.

In general wave-functions spread and propagate. However, there are certain situations where they cease to do so. Those situations are equivalently interpreted as frozen or localized quantum particles. In the context of condensed matter physics, this localization---the vanishing of the group velocity for a large class of states---is related to the appearance of flat bands in the band structure of a quantum system. The flat bands are important occurrences for multiple reasons. One of them is that on a flat band the kinematics of a system is non-existent and therefore the physics is completely governed by the interaction terms which are responsible for many exotic states of matter. Therefore, one expects that a flat band is a bedrock for finding exotic states. The appearance of flat bands is also, at times, a puzzling phenomenon. For example, the recurrent flat bands in twisted bilayer graphene for different twist angles are not yet completely understood, even at the single particle level, and they are surprising enough that the angles at which they appear are called “magic” angles. Here, the field theoretic approach to these interesting phenomena is presented.

The nature of dark matter (DM) remains one of the most profound open questions in fundamental physics. In this thesis, we develop and apply novel precision measurement techniques to probe DM across a broad range of candidate masses and interaction strengths. For weakly interacting massive particle (WIMP) DM, we present a new directional detection scheme based on solid-state quantum sensing in diamond. For ultralight bosonic DM, we introduce a novel experimental concept--GALILEO--which employs electro-optics and resonant interferometry to search for DM–induced oscillating electric fields. To probe ultra-heavy DM, we develop a geological detection method that maps extended damage tracks in ancient quartz using electron microscopy, leveraging billion-year exposure times for enhanced sensitivity. Finally, we analyze gravitational wave signals from double white dwarf binaries, treating them as a distributed array of galactic accelerometers capable of dynamically measuring the Milky Way’s gravitational potential.

Together, these complementary approaches demonstrate the potential of precision measurement science to expand the search for DM. They highlight the powerful interplay between quantum technologies, materials science, and astrophysics in tackling some of the most fundamental mysteries of the universe.

Quantum information science is a promising, interdisciplinary field focusing on both understanding and utilizing quantum systems. Two major paradigms of quantum mechanics are discrete variable (finite dimensional) systems, such as qubits and qudits, and continuous variable (infinite dimensional) systems, such as bosonic modes. In this dissertation, we explore the properties, protocols, and applications of both discrete and continuous variable systems.

In the first part of this dissertation, we study Hilbert space structures called quantum state designs, which are small ensembles of quantum states that mimic properties of the full space. While such designs are well-studied in the discrete variable setting, we show that they can also be defined and constructed in the continuous variable setting. Using specific multimode ensembles, we demonstrate continuous variable shadow tomography protocols which allow for efficient estimation of expectation values of many observables. Additionally, we use these ensembles to define notions of average and entanglement fidelities of continuous variable quantum channels, and we derive an explicit relationship between them that resembles the analogous relationship in the discrete variable setting.

Meanwhile, on the discrete variable side, we construct a theory of designs on the torus and find general methods for constructing them in arbitrary dimensions. Using these toric designs and their relationship to quantum state designs, we construct many new and explicit families of quantum state designs. Furthermore, we use toric designs to prove various structure theorems about complete sets of mutually unbiased bases.

In the second part of this dissertation, we examine entanglement in continuous variable systems. Specifically, we analytically derive average and typical entanglement properties, as measured by all integer Rényi entropies, of random ensembles of Gaussian states outputted from a Gaussian boson sampling device.

Finally, in the third part of this dissertation, we examine the use of qubit systems for resolving frequency spectrums in signal processing applications. Specifically, we show that a classical signal whose spectrum contains closely spaced frequencies can be resolved by coupling the signal to a qubit and performing a superresolution protocol. We find general conditions for a protocol to exhibit superresolution and show various analytic and numerically-optimized protocols that achieve superresolution.

Quantum many-body systems host a variety of exotic phases, which are described as the deconfined phase of an emergent gauge theory. Such phases in the context of spin systems go by the name Quantum Spin Liquids (QSLs). Often, the same features that make them interesting also make them hard to detect experimentally. This thesis is a collection of works aimed at connecting the defining theoretical properties of such phases to experimentally accessible observables, both in the setting of solid-state materials as well as quantum devices.

The main theme of the first part of the thesis is magnetic monopoles of emergent compact U(1) gauge theories that describe certain QSLs, namely Quantum Spin Ice and Dirac Spin Liquid in three and two spatial dimensions respectively. The condensation of monopoles drives a deconfinement-confinement phase transition in the gauge theory, and in the context of spin systems, drives transitions from QSL to ordered phases. We exploit this understanding to propose a ``Monopole Josephson Junction" scheme to test if a candidate material is a Dirac Spin Liquid. A key component of our detection scheme is Raman Scattering.

In the second part of the thesis, we explore quantum optics techniques to probe correlated quantum materials. In optical experiments, the photonic observable measured is usually the intensity or photon number operator of inelastically scattered light. We ask a general question -- what can we learn about a correlated material, given access to other photonic observables like quadrature and correlation between pairs of photons (G2)? We develop a general formalism to map such photonic correlation functions to electronic ones. Focusing on the Fermi-Hubbard model at half-filling, we show that such correlators can be used to probe spin-charge correlations, and to detect QSLs by detecting spin chirality and existence of fractional statistics.

Cells constantly interact with their physical environment by sensing and responding to mechanical and topographical cues. These cues span multiple scales, from subcellular interactions with the extracellular matrix to population-scale confinement in morphogenesis. Central to this process is the actin cytoskeleton, which serves as both a local force generator and a medium for signal integration and propagation. In this dissertation, I combine multiscale computational modeling with quantitative imaging to investigate how actin dynamics drive physical sensing from the scale of single protrusions to collective cellular behavior.

The actin cytoskeleton is the primary mechanism for generating forces that cause cell protrusions and guided migration. Using 12Z cells as a model of endometriosis, we examine how exposure to the biochemical signal estradiol alters actin organization and, consequently, cell morphology. High-resolution 3D imaging reveals that estradiol treatment increases protrusion size and disorder in actin dynamics, consistent with enhanced cellular invasiveness. These findings highlight how chemical signals modulate mechanical output through actin-based protrusions, reinforcing the role of actin as a key transducer of biochemical cues into physical motion.

At the subcellular scale, we use a 3D phase-field model to illustrate how cells exhibit unidirectional migration on asymmetric nanotopographies, with directionality controlled by actin polymerization rate and topographic scale. In this model, an asymmetric substrate alone can cause spontaneous polarization and reproduce the shape and guidance morphologies observed experimentally. These predictions align with a reanalysis of D. discoideum experiments, revealing that guidance on subcellular sawteeth depends on both cell velocity and feature height. This agreement indicates that membrane deformation and local curvature sensing, driven by actin forces, are sufficient to bias migration in complex microenvironments.

To study how the actin cytoskeleton responds to chemical cues found in the extracellular matrix, we analyze epithelial cell migration on collagen-coated nanoridges. On nanoridges, collagen IV enhances actin alignment and cell elongation; however, actin guidance remains decoupled from the direction of migration. Therefore, additional mechanisms, such as focal adhesion dynamics, may contribute to directional sensing.

At larger scales, we develop a scalable 2D multicellular phase-field model incorporating excitable actin dynamics. This framework enables simulations of thousands of deformable cells on consumer hardware. The model spans a range of scales, allowing cell interaction, long-distance wave propagation, and information exchange. In this model, excitable intracellular mechanics, along with local physical interactions, can lead to emergent synchronization and local sensing of the shape of large-scale confinement.

Together, these findings suggest that actin serves as a mechanochemical interface for multiscale environmental sensing by driving local protrusions, integrating physical signals, and enabling collective coordination through excitable dynamics. Actin polymerization additionally acts as an upstream regulator of other cell functions, which opens avenues for future experimental studies on the effects of actin synchronization and pulsing on biophysical behavior. By linking cytoskeletal signaling to large-scale coordination, this work lays the foundation for identifying new physical mechanisms underlying biological processes that require coordination, such as metastasis and tissue morphogenesis.

We characterize the performance of current quantum dot spin qubit devices for small quantum simulations, demonstrate a new theoretical framework for the modeling of the qubit charge stability diagram, and propose a new qubit design to extend coherence times and reduce leakage errors in exchange qubits. First, we show that silicon quantum dot spin qubits can effectively simulate discrete time crystals with clear signatures that appear even in small arrays, where charge noise—typically detrimental to qubit performance—actually stabilizes the time-translation symmetry breaking phase. Second, we develop full configuration interaction methods to accurately model multi-electron quantum dots, revealing significant many-body effects that enhance tunneling couplings and improve device characterization beyond single-electron approximations. Finally, we introduce the Singlet-only Always-on Gapless Exchange (SAGE) qubit architecture, a four-electron encoding that eliminates sensitivity to local magnetic fields while maintaining all-electrical baseband control, and suppressing leakage. The SAGE qubit offers a promising pathway toward ultra-scalable quantum computation with spin qubits.

Atomically-precise acceptor-based qubits are promising candidates for spin-based quantum computing due to their inherently strong spin-orbit interaction and the feasibility of fast electrical control using gates. Despite their theoretical promise, experimental studies of acceptor qubits have been limited due to challenges in fabrication and process development. Throughout my Ph.D. research, I addressed these challenges by developing comprehensive fabrication processes combined with quantum tunneling and transport measurements to investigate atomically-precise acceptor doping and devices, culminating in the realization of the first atomically-precise single-hole transistor (SHT), which is a critical component for single-acceptor-atom qubit readout.

Initial investigations focused on Al dopants in Si, where I conducted detailed investigations into AlCl₃ adsorption on Si(100) surfaces and subsequent annealing effects, utilizing scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional theory (DFT) calculations. Magneto-transport measurements conducted on AlCl₃ exposed Si samples after dopant incorporation and Si capping failed to produce a noticeable electrical activation of Al dopants, despite Al concentrations exceeding 10¹⁹ cm^-3 in the δ-doped region, as verified by secondary ion mass spectrometry (SIMS).  This result, combined with the observation that AlCl₃ readily adsorbed and formed extended chlorinated aluminum chains on the surface post-annealing, points towards a dopant deactivation process.  Ultimately, this limits the suitability of AlCl₃ for practical atomically-precise doping applications.

Studies with BCl₃ demonstrated barrierless dissociative adsorption onto Si surfaces. Experimental validation through STM, SIMS, and Hall measurements confirmed ultrahigh doping densities, exceeding 10²¹ cm^-3, could be achieved with minimal thermal processing. Atomically-precise, area selective deposition was demonstrated utilizing STM-patternable, monatomic resists of either hydrogen or chlorine, enabling the fabrication of atomic-scale wires that exhibit ohmic conduction down to mK temperatures.

I studied the mechanism of hole tunneling in an atomically-precise SHT, in which the dimensions were defined with sub-nanometer precision utilizing STM-based lithography. Coulomb peaks and Coulomb diamonds were readily observed and indicative of single-hole resonance tunneling associated with 310 ± 20 boron atoms confined within a 13 ± 0.5 nm x 14 ± 0.5nm region in Si.  Analysis using the Wentzel–Kramers–Brillouin (WKB) approximation and capacitance modeling via a three-dimensional Poisson solver highlighted that hole tunneling was dominated by carriers with the lowest effective mass, i.e. light holes. DFT calculations further supported these observations. These results not only provide fundamental insight into the tunneling mechanism of holes in Si, but they pave the way for future explorations and measurements of single acceptor atom qubits in Si.

This dissertation combines work from several disparate fields of research to explore the epistemic value of complexity and care in knowledge generation in physics. Complexity means intentionally constructing models that account for multiple interacting effects, yielding deeper insight and new research directions. Care means viewing physics as a fundamentally human endeavor and recognizing that the human aspects are as important as the technical aspects for rigorous and sustainable progress in physics.

The dissertation begins with experimental results using Rydberg atoms. Rydberg atoms, with their long lifetimes, sensitivity to electric fields, and strong interactions, have found use across atomic physics, from fundamental physics investigations to emerging quantum technologies. In this dissertation I describe efforts to optimize a Rydberg-ensemble single-photon source, which resulted in an accurate model of Rydberg spin-wave dephasing. I then show evidence of enhanced Rydberg interactions using microwave dressing. This is a first step toward many possible applications, including fully tunable interactions, the exploration of non-equilibrium phenomena, the generation of nonclassical states of light, and improved atom-photon entanglement for quantum networking.

The second part of this dissertation explores two photonic devices critical to quantum science and technology. First, we describe an algorithm for reconstructing the photon number distribution of light pulses using a single single-photon avalanche detector. We achieve high-fidelity reconstruction of both coherent and anti-bunched pulses whose duration and correlation timescales are both at least a few detector dead times in duration, and we explore the limits of the algorithm at high input photon rates. Second, we describe an \emph{ab initio} model of the random and time-varying birefringences of optical fibers. Environmentally induced drifts make this a serious challenge for polarization-encoded quantum networks, which is becoming crucial to understand as a new generation of quantum networks comes online. A first-principles model of the birefringences in fibers will allow for determinations about the suitability of installed fibers for quantum networking applications and for development of mitigation methods and compensation strategies.

In the final part of this dissertation, I describe the development and results of a national-scale study of physics and astronomy graduate student mental health. Mental health challenges in academia are well-documented, but the mental health of graduate students remains understudied, especially in physics and astronomy. Our sample reports clinical levels of anxiety and depression at 5-7 times the rate of the general population. Female and non-binary students in our sample report more symptoms of anxiety, depression, and impostor phenomenon than male students. Using structural equation modeling, we find that loneliness is an especially strong predictor of these mental health issues in our sample, and we clarify pathways by which advisors support their graduate students. Thus these results suggest specific ways that peers, faculty, and departments can support graduate student mental health.

The LIGO–VIRGO–KAGRA collaboration has reported 90 confirmed gravitational-wave detections and nearly 200 high-confidence triggers across four observational runs, primarily originating from coalescing black hole and neutron star binaries. This research investigates how the intrinsic properties of compact objects influence their dynamics and gravitational-wave emission, employing worldline effective field theories and black-hole perturbation theory, with particular emphasis on scattering processes in General Relativity.

The presentation will begin with an overview of the research conducted during the PhD and the main results obtained. The second part will focus more specifically on the the research on extraction of tidal effects in compact-object binaries by studying gravitational-wave scattering off isolated compact objects. I will describe how this process is formulated within the worldline framework and in black-hole perturbation theory, and how it enables the extraction of tidal response coefficients in relativistic compact objects. Key results on the tidal response of black holes and neutron stars will be presented.

Topological phases of matter have long been a central theme in condensed matter physics. When subject to certain symmetries, these phases are classified by topological invariants that often take fractional, quantized values. Despite significant theoretical advancements, major open questions remain regarding the computation of these invariants in systems with crystalline symmetry, nonzero Chern number, or fractional quantum Hall states with fractional Hall conductivity.

The first part of this dissertation establishes the necessary theoretical background, defining symmetry operators, geometrical measures, and topological actions used to determine crystalline topological invariants.

The second part focuses on extracting these invariants numerically for invertible fermionic states in multiple ways. We will discuss the properties of these invariants such as how they determines the universal charge response of crystalline defects and boundaries and how they depends on an origin o in real space. Concrete numerical methods are demonstrated using the Hofstadter model, which exhibit non-zero Chern number and magnetic field. These invariants, together with several established invariants in the literature, gives a complete classification of ground states and reveal novel colorings of the Hofstadter butterfly.

The third part of this dissertation extends the calculation of crystalline topological invariants to fractional quantum Hall states, such as the 1/2-Laughlin state constructed by projecting parton states onto the same position. We show that the numerically extracted values of these invariants align with theoretical predictions from conformal field theory and G-crossed braided tensor categories

The center of our Galaxy is an intriguing region in astrophysics, providing a unique

opportunity to study various astrophysical processes. However, our line of sight is ob-

scured by dense layers of dust and gas, making optical emission observation impossible.

Fortunately, we can observe other portions of the electromagnetic spectrum, such as radio,

X-rays, and gamma rays. The latter serve as probes of cosmic-ray acceleration to extremely

high energies and, in theory, for indirect Dark Matter (DM) detection. This dissertation an-

alyzes gamma-ray data from the Galactic Center (GC), obtained with the High-Altitude

Water Cherenkov (HAWC) Gamma-Ray Observatory.

The HAWC Observatory, situated on the Sierra Negra volcano in Mexico at an altitude

of 4,100 m, detects gamma rays with energies from 0.1 to greater than 100 TeV. It has a

wide field of view of about 2 sr, and with an operational duty cycle of over 95%, it observes

two-thirds of the sky daily. The observatory uses the water-Cherenkov detection technique

to detect Cherenkov emission from secondary air-shower particles. This study presents

improvements to the reconstruction algorithms that retrieve the properties of the primary

gamma rays. In particular, the angular resolution and background rejection have improved

by a factor of four for gamma-ray events coming from high-zenith angles and with energies

above 40 TeV. Thanks to these improvements, HAWC can detect the GC.

Although multiple sources of cosmic-ray acceleration to PeV energies, known as Pe-

Vatrons, have been proposed within the Galaxy, they remain insufficient to fully account

for the observed flux. In this context, the GC was proposed as one of the main Galactic

PeVatrons with a power-law spectrum that extends up to 50 TeV without a cutoff. Here,

we present, for the first time, observations of gamma rays with energies above 100 TeV,

which we suggest originated from PeV protons—accelerated in the GC—that interact with

the dense ambient gas. While the angular resolution of HAWC at this high zenith angle is

not enough to distinguish the PeVatron, we provide the first confirmation of its existence.

The GC is also one of the most promising candidates for indirectly detecting DM via

gamma rays. While the nature of DM remains a fundamental question in modern physics,

Weakly Interacting Massive Particles (WIMPs) are considered potential candidates for DM

and naturally emerge in several extensions of the Standard Model (SM) of particle physics.

The relic density of thermally produced WIMPs in the early Universe can account for all

the DM observed in the Universe, as measured from cosmological observations. In theory,

WIMPs self-annihilate in dense astrophysical environments, like the GC, producing gamma

rays in the final state from processes such as hadronization, radiation, and decay of SM

particles. We conduct a follow-up study of the above analysis and compare the spatial

and spectral morphology of the residual gamma-ray emission to the one theorized for DM

annihilation. Finding no significant emission, we place for the first time to date upper

limits at the 95% confidence level on the velocity-weighted cross section, for

DM particle with masses well above 70 TeV using GC gamma-ray data.

Moiré transition metal dichalcogenide (TMD) bilayers have emerged as a versatile platform for exploring a wide range of correlated electronic phenomena. In optical studies of these semiconducting systems, excitons—bound electron-hole pairs—play a crucial role by linking electronic correlations to optical responses. This thesis develops theoretical frameworks to understand how excitonic behavior interplays with various correlated states in moiré TMD bilayers and the resulting implications for optical measurements.

We begin by investigating the interaction between a single moiré exciton and Wigner crystal states formed by doped electrons. Focusing on systems with repulsive electron–exciton interactions, we discuss a scenario where excitons move within the complementary lattice of the charge-ordered electrons. As different Wigner crystal configurations emerge at specific electron filling fractions, the effective exciton lattice changes accordingly, giving rise to distinct spectral and topological features. These characteristics can serve as optical signatures of the underlying charge order, and we propose a momentum- and polarization-resolved reflection experiment to detect them.

Next, we turn to undoped bilayers hosting multiple moiré excitons. While prior work often models these systems using a Bose-Hubbard framework, we show that their commutation relations deviate from those of conventional bosons. Instead, the excitons obey algebra similar to that of angular momentum operators, resulting in a finite Hilbert space and limiting local exciton occupancy to two or three, depending on the bilayer's specific parameters. We demonstrate that this occupancy constraint could manifest in high-intensity optical pumping experiments.

Finally, we explore exciton dynamics in a doped heterobilayer where the topmost valence moiré band forms an antiferromagnetic Mott insulator. We present a theoretical model describing the coupling between the exciton and the spin background, revealing that spin fluctuations substantially narrow the exciton’s effective bandwidth—by orders of magnitude compared to its non-interacting counterpart. This suppression in mobility provides a measurable contrast, which we suggest can be probed through exciton diffusion experiments.

Superconducting circuits are at the forefront of quantum computing and quantum sensing technologies, where accurate modeling and simulation are crucial for understanding and optimizing their performance. In this dissertation, we study modeling techniques and novel device designs to advance these technologies, focusing on efficient simulations, direct velocity measurement, and nonreciprocal devices for quantum information processing.  First, we investigate the use of discrete variable representations (DVRs) to numerically represent superconducting circuits, exploring their use and effectiveness in several prototypical examples. We find that not only are these DVRs capable of achieving decoherence-accurate simulation, i.e., accuracy at the resolution of experiments subject to decay, decoherence, and dephasing, they also demonstrate improvements in efficiency with smaller basis sizes and better convergence over current standard approaches, showing that DVRs are an advantageous alternative for representing superconducting circuits.

We then consider a specific quantum sensing application, direct velocity measurement in superconducting circuits. We propose and characterize theoretical models for backaction evading, direct velocity measurement that utilize traditional electric and magnetic transducers. We consider the readout of this signal via electric or magnetic field sensing by creating generic models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme --- voltage or current --- for each mechanical detector configuration implies access to either the position or velocity of the mechanical sub-system.

Finally, we explore the application of superconducting circuits in nonreciprocal devices, such as circulators. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large magnetic fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order --- such as the XY model --- can be realized at much lower magnetic fields by using arrays of superconducting islands connected by Josephson junctions. Here we show that the quantum-coherent motion of a single vortex in such an array suffices to induce nonreciprocal behavior, enabling a small-scale, moderate-bandwidth, and low insertion loss circulator at very low magnetic fields and at microwave frequencies relevant for experiments with qubits.

Weakly Interacting Massive Particles (WIMPs) remain one of the most-well motivated dark matter candidates. Liquid Xe (LXe) time projection chambers (TPC) are the leading technology for probing the WIMP mass range. The LUX-ZEPLIN (LZ) experiment is a 10 tonne LXe TPC searching for the elusive WIMP dark matter. As detector masses increase to maximize sensitivity, background sources in the Xe, such as 85Kr and 39Ar, must be reduced to meet background requirements. These species are more difficult to quantify and require more stringent monitoring compared to previous generations of experiments. In this work, the techniques used to monitor 85Kr and 39Ar during commissioning and through LZ's WIMP Search 2024 science run (WS2024) are discussed. The natural Kr concentration during WS2024 is measured to be 182 +/- 26 ppq (g/g) (Kr/Xe) using a mass spectrometry technique. A complementary search for an excited state decay of 85Kr measured a natural Kr equivalent concentration of 124 (+44) (-37) ppq (g/g) (Kr/Xe). The natural Ar concentration during WS2024 is measured to be 1.10 +/- 0.18 ppb (g/g) (Ar/Xe). LZ has set a world leading limit on the interaction cross section across the expected WIMP mass range with a minimum of 2.1 * 10^-48 cm^2 at 36 GeV/c^2.

Systems containing large numbers of electrons can exhibit surprisingly complex and rich dynamics. In this dissertation, we ask: What is the minimum necessary detail in measurement or data-driven modeling and simulation to capture complex dynamics manifesting from these systems? To answer this, we integrate experiment, simulation, and theory to understand their complex dynamics. In this dissertation, we examine two such systems: (i) a superparamagnetic tunnel junction (SMTJ) and (ii) charged-particle beam dynamics.

We first consider the deterministic-stochastic behavior of a constant-current driven SMTJ, where we create a measurement-driven overdamped Langevin model capturing statistical properties of the device. We show both how this model captures device statistics across time scales and how it can be refined to capture higher-order behavior.

We next examine the centroid motion of a charged-particle beam and propose a method for understanding and predicting it using an interpretable, data-driven approach whose output is directly identifiable to terms in underlying low-dimensional evolution equations. We derive the evolution equations solely on the basis of data—with no recourse to an underlying first principles model. We compare and contrast our methodology with both a machine learning technique and a first principles model, and we show that we can learn interpretable equations for nonlinear beam dynamics at lower computational cost while achieving comparable accuracy.

Lastly, we investigate the phase space evolution of a charged-particle beam. Accurate knowledge of the phase space at beam creation is crucial for understanding and predicting beam dynamics. We measure a velocity space modulation to initialize the phase space of first principle simulations and capture beam statistics and internal beam structure­­­­­­­­­­­­—resembling a cruciform—with high fidelity. This contrasts with both employed first principles models—which do not account for beam structure as they assume a uniform beam cross section—and simulations using ideal phase space distributions. Finally, we demonstrate sensitivity to beam and lattice parameters varied within experimental measurement error.

Superconductors host vortices when exposed to a magnetic field exceeding their first critical field Bc1. Understanding the dynamics of vortices is crucial for optimizing the performance of various applications of superconductors, including superconducting radio-frequency (SRF) cavities and superconducting digital and quantum circuits. In this thesis, a near-field magnetic microwave microscope is employed to locally stimulate superconductors with an intense rf magnetic field and measure the local nonlinear microwave response. Under the microscope probe, two distinct vortex-related phenomena are observed: the nucleation of rf vortices and the motion of pre-existing trapped vortices. To interpret the measured response, toy models of superconductors with local defects are introduced and analyzed using Time-Dependent Ginzburg-Landau (TDGL) simulations of probe/sample interactions.

This dissertation is divided into two parts. The first part investigates the nucleation of single/few rf vortices associated with surface defects by studying the third-harmonic response P3f produced by the superconductor under intense stimulus at frequency f. Seven Nb/Cu films, grown under different deposition conditions by collaborators at CERN, are measured. Their surface defect properties related to rf vortex nucleation are compared. The second part explores the dynamics of trapped vortices under oscillating magnetic fields by studying the second-harmonic response P2f. A superconducting Nb film with an antidot flux pinning array is measured. The results show that this measurement technique provides access to vortex dynamics at the micron scale, including depinning events of a small number of trapped vortices and spatially-resolved pinning properties. These findings contribute to a deeper understanding of microwave superconductivity and vortex-induced nonlinearities, shedding light on the fundamental interactions between rf fields, magnetic vortices, and defects in superconductors. Furthermore, they offer new insights into the design and optimization of superconducting devices for microwave applications.

As artificial intelligence (AI) systems grow increasingly powerful and permeate every aspect of our lives, their impact on both individuals and society is an urgent concern. Questions of safety and robustness in AI stem largely from our limited understanding of deep learning. Research in this domain has traditionally followed two parallel paths: an empirical approach that prioritizes practical advancements and a theoretical approach that seeks a mathematical understanding from first principles. Despite notable progress, a significant gap remains between deep learning practice and its theoretical underpinnings. This dissertation advocates for a phenomenological approach to understanding AI systems -- one that integrates empirical observations with theoretical model-building. This methodology has been instrumental in the physical sciences, and it holds similar promise for advancing the science of deep learning. Over two broad parts, this work demonstrates the effectiveness of this approach in characterizing model architectures and their emergent capabilities.

In the first part, we explore how signal propagation analysis in large-N limits can inform the design and initialization of model architectures. We develop a diagnostic observable that distinguishes between ordered and chaotic behaviors in neural networks, guiding optimal parameter initialization for training. Our analysis establishes the theoretical soundness of this observable in simple networks and confirms its empirical utility in state-of-the-art architectures. The findings reveal an architecture design paradigm that eliminates the need for careful initialization, shedding light on widely used heuristic practices. Additionally, we introduce an algorithm that automates initialization across diverse model architectures, enhancing their trainability.

In the second part, we highlight the importance of the systems identification approach for characterizing AI systems. We explore several stylized setups where model capabilities emerge as a function of compute, data quantity, and data diversity. Using arithmetic and cryptographic tasks as examples, we demonstrate that emergent abilities such as grokking and in-context learning arise alongside the formation of interpretable structures within the model’s parameters, hidden representations, and outputs. Through targeted experiments, we identify these structures using (i) black-box probing, which examines model responses to characteristic inputs, and (ii) open-box analysis, which leverages curated task-specific observables and metrics to study internal model states.

This dissertation promotes a paradigm for understanding deep learning that complements both heuristic-driven and hypothesis-driven approaches. By integrating experimental methodologies and analytical tools from established scientific disciplines, this framework has the potential to steer the field toward safer, more robust, and more efficient AI systems.

In recent years, quantum experiments have become increasingly precise, fast, and capable of high resolution. Particular interest has been given to quantum control, which aims to prepare, manipulate, and steer quantum states toward desired outcomes. Common applications of quantum control include state preparation for quantum computing algorithms, protocols to implement nanoscale machines, and feedback to guide a system's evolution. Feedback involves collecting information from quantum measurements, then acting on the system based on measurement outcomes. The standard measurement model in quantum mechanics is the projective measurement, which destroys quantum coherence by causing the wave function to collapse to a subspace spanned by the eigenstates of the measured operator.

This thesis explores the theory of weak measurement processes, a class of measurement protocols that extract information from a quantum system while (partially) preserving coherence. The weak measurement protocol has a tunable parameter that controls the information obtained per measurement cycle and the disturbance (decoherence) introduced into the quantum system. Using this nondestructive form of measurement, one can extract information during the system's evolution and apply real-time feedback to drive the system's evolution to specific target states. A general master equation is derived to describe continuous feedback using weak measurements with general filtering processing. Particular cases of low-pass and band-pass filters are studied in detail and applied to a harmonic oscillator cooling protocol. Results show that ground-state cooling of the quantum harmonic oscillator can be achieved.

Finally, this dissertation discusses an experimental and computational project that uses machine learning to estimate the temperature and the number of atoms of a cold atomic cloud. The goal is to use non-destructive measurements to infer hidden properties of the atomic ensemble without disturbing the atomic trap. Results show that reasonable accuracy can be achieved using various neural network architectures, depending on the complexity of the input data. The accuracy and responsiveness of the trained models make them suitable for real-time estimators that can be used in closed-loop feedback.

Since the 1973 announcement of the initial Vela detection of Gamma Ray Bursts (GRBs) in 1967, these powerful events have been of significant interest. The study of GRBs has advanced our knowledge of plasma physics, particle physics, cosmology, among many other fields. However, even with the advancement in understanding gained through various detections, both multi-wavelength and multi-messenger, there is still much to be learned by observing these transients in as many different ways as possible. This dissertation will explore the development of instrumentation (RIMAS and PRIME), operational software, data reduction software, and observations aimed at furthering the study of GRBs.

RIMAS is a near-infrared imager spectrometer operating in wavelengths from 0.97 to 2.37 µm, and will be installed on the 4.3 m Lowell Discovery Telescope (LDT) in Happy Jack, Arizona. Among other features, RIMAS has four broad band filters (Y, J, H, K), and three spectral modes (R30, R300 and R5000). Completing this instrument required the development, integration and testing of multiple detector readout systems, cryogenic systems, spectral and imaging modes, communication systems, and cooling systems. Furthermore, software needed to be developed to reduce RIMAS data so that it will be ready to contribute to scientific discoveries shortly after commissioning. Due to the development of this software, observers will quickly obtain high signal-to-noise exposures, astronomically and photometrically calibrated stacked images, and one-dimensional spectra that is flux and wavelength calibrated.

PRIME is a 1.8 m telescope with 1.56 square degree FOV (0.5"/pixel) operating in the NIR (0.82-1.78 µm) located in Sutherland, South Africa at the South African Astronomical Observatory (SAAO). The primary science objectives for PRIME are to perform a time domain survey of the Galactic Bulge for the purpose of observing microlensing events caused by transiting exoplanets. In doing so, it will support the Nancy Roman Space Telescope (RST) mission by taking baseline measurements of this field before RST launch, while testing the performance of RST package H4RG-10 detectors. After RST launch, PRIME will perform simultaneous observation with RST of the Galactic Bulge to perform parallax measurements. PRIME is also continuously available for Target of Opportunity (ToO) observations, making it a powerful tool for observing GRB and GW counterparts. Since commissioning in October 2022, PRIME has been observing a time domain survey of the Galactic Bulge searching for microlensing events, observing high energy transients (GRBs, X-ray bursts, gravitational waves, and supernovae), and performing an all-sky survey in J-band. During the course of this thesis work, the development of PRIME's camera greatly mirrors that of RIMAS, with lessons learned shared between them. Most notable in this development is the integration and testing of PRIME's detectors and detector readout system. This is the first instance of these detectors and electronics being used on-sky, and as such required the development of custom software and thorough testing.

Beyond these instrumentation efforts, photometric and spectroscopic observations were performed in the optical for various GRB afterglows, GRB host galaxies, and GW counterpart candidates using LDT's optical imager, LMI, and optical spectrograph, DeVeny. Multiple high energy transients (GRBs, X-ray Bursts, LVK probability fields) were also observed using the recently commissioned PRIME telescope. These efforts have resulted in many GCN circulars, and contributed to multiple papers.

The study of quantum computers and quantum algorithms has captured the attention of physics globally in recent decades. While some researchers are working towards constructing fault-tolerant large-scale quantum computers, others are theorizing about the capabilities of these new computers and developing quantum algorithms to leverage their increased abilities. This dissertation engages with the second area of research concerning quantum algorithms. The first part of this dissertation discusses quantum algorithms for state preparation, with a focus on thermal state preparation. A selection of other state preparation methods is briefly summarized before a novel method of thermal state preparation is laid out wherein a so-called heat pump is employed in a technique of active cooling. The second part of this dissertation discusses quantum algorithms that aim to address the problem of gauge violation during the simulation of lattice gauge theories. The problem of gauge violation in both quantum analog and digital simulations is presented before two related methods are delineated. These methods leverage the quantum Zeno effect with frequent measurements on a system's physical subspace to keep the system's state physical throughout the course of a simulation. Furthermore, the properties of gauge transformations are utilized to help curtail the growth of unwanted unphysical amplitudes.