Physics and Astronomy

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This is the collection for the University of Waterloo's Department of Physics and Astronomy.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

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Structured Wavefunctions for Precision Quantum Metrology
(University of Waterloo, 2025-10-20) Kapahi, Connor
In this thesis, several projects from biomedical optics measurements of the retina to precision gravimetric designs with neutron interferometers are presented, united by the common theme of applied quantum information techniques to develop next-generation precision metrological instruments. In particular, we introduce theoretical tools for analyzing neutron optical experiments and highlight parallels between neutron and light optics. These tools are applied to a new neutron prism design, demonstrating significantly higher transmission than traditional designs. Designs for devices applying these techniques, including a neutron Fresnel prism, spectrum analyzer, and spin collimator, are discussed. Potential advantages in neutron flux and spectrum resolution are quantified for these designs. The isometry between neutron spin and the polarization of light is exploited to validate the neutron spin collimator experimentally. Applications of structured states of light and experiments applying spin-orbit states to create patterns in the human visual system are described. Results demonstrate an increase in the perceived extent of these patterns, from 3° for Haidinger's Brush to 10° for a spin-orbit state. Work demonstrating a new method of generating a lattice of spin-orbit states in light is applied to neutron optics. Throughout the preceding experiments, methods of modeling neutron optics experiments with light and a semi-classical path-integral approximation have been developed. These methods are then applied to design an experiment that measures the gravitational constant using a neutron interferometer. A three-phase grating moiré interferometer (3-PGMI) design is first tested with infrared light. The deflection caused by a wafer sample is measured with the 3-PGMI and found to match direct measurements. The path-integral model is then applied to determine the uncertainty in the gravitational constant that can be achieved with a near-term measurement with a neutron 3-PGMI. An experiment to measure the gravitational constant is described, with an uncertainty budget, resulting in a measurement to 150 ppm. Potential corrections to previous experiments measuring the gravitational constant, due to lunar gravitational forces are quantified. Future applications of the tools and techniques described in this thesis are then discussed.
Translocation-Induced Shape Transitions in Vesicles using a Neural Network-Based Solver for the Helfrich Model
(University of Waterloo, 2025-10-16) Choheili, Soorna
This thesis discusses our efforts to model the translocation of an enclosed lipid bilayer membrane (vesicle) through a circular pore. First, we will discuss the study of lipid bilayers, introduce the standard model for representing the energy of a membrane, and provide background on the many theoretical and experimental efforts in the field of membrane modeling. We then review the relevant theoretical and practical considerations regarding the simulation of vesicles and translocation, and implement a neural network-based solver for a scalar phase field. We will proceed to detail our efforts to characterize each constraint imposed on the vesicle throughout the translocation and model them within the context of the solver. Following this, we provide a variety of visual snapshots of the translocation process showing different classes of translocation and the resulting behavior of each. Equally important is the quantitative analysis of the energy landscape traversed by the vesicle, where we chart the induced bending energy imposed upon it by the narrow pore. Additionally, we introduce two types of external effects that modify the energy landscape and illustrate their impact on the total vesicle energy throughout its passage. We then map the results out onto the relevant parameter space to give a picture of where the thresholds between qualitatively different behaviors lie. As a final demonstration of our model’s capabilities, we estimate the time of passage of the vesicle by modeling it diffusively using the energy landscape to calculate the effect of narrower pores on the time to translocate. This model successfully demonstrates explicit phase transitions between stable vesicle states and maps out the energy landscape throughout the unstable regime under the effects of translocation.
Vacuum assembly, atomic source development, and micromotion studies for a trapped Ba+ based quantum processor
(University of Waterloo, 2025-09-22) Khatai, Ali
Trapped-ions are one of the leading platforms for quantum information processing, due to their long coherence times and high-fidelity State Preparation and Measurement (SPAM) and gate operations. However, implementing a trapped-ion system with many desirable features such as Ultra-High-Vacuum (UHV), High-Optical-Access (HOA), and a high trapping probability presents significant technical challenges. These features are critical for enabling complex quantum simulation experiments, including simulations of spin-1/2 systems and beyond, by leveraging the multiple internal states of barium and tunable spin–spin interactions. High optical access is required to deliver tightly focused beams for site-resolved control and inter-ion coupling, while UHV conditions are essential for achieving long ion lifetimes necessary for stable, large-scale simulations. Achieving such optical access, which is vital for both coherent gate operations and high numerical aperture fluorescence collection, whilst maintaining vacuum integrity presents substantial engineering challenges. This thesis presents the construction of a vacuum chamber system intended for an individually addressable 16-qubit quantum processor based on barium-133 ions confined in a microfabricated surface-electrode ion trap. Although the complete processor has not yet been realized, the chamber has been assembled to support its future implementation. The microfabricated surface-electrode ion trap features ∼ 100 electrodes that require independent control of static voltages for precise tailoring of the confining electric potential. The experimental setup was designed to provide high optical access and to reach base pressures in the low 10^(−11) mbar range, thereby minimizing ion–background gas collisions. This is achieved by centrally mounting the trap within the vacuum chamber, a departure from conventional flange-mounted designs. To bring in-vacuum electrical connections to ∼ 100 trap electrodes, a custom implementation of an in-vacuum wire harness is described that enables reliable electrical connectivity to the centrally mounted surface electrode ion trap. The development of this wire harness enabled us to reach UHV with a pressure of ≈ 3 × 10^(−11) mbar. The successful development of this wire harness demonstrates that it is possible to create a UHV compatible wiring solution using commercially available components for a surface-electrode ion trap suspended at the center of the vacuum chamber. This centrally mounted design provides both high optical access and high conductance to vacuum pumps, enabling individual ion addressing and long ion lifetimes, which in turn facilitate more complex quantum simulation experiments. In addition, a multispecies ablation target was developed that incorporates both radioactive barium-133 and metallic barium to enable ion loading at lower trap depths, addressing a common challenge in surface-electrode ion traps. The velocity of the atomic plume generated from barium metal ablation targets was measured and compared to that of BaCl_2 targets. Although we were unable to definitively measure the effective temperature and peak velocity of the atomic plume generated from barium metal, the neutral fluorescence measurements from the barium metal targets indicate a larger number of slower moving atoms compared to BaCl_2 targets. The lower speeds of the atoms generated from metal targets is also plausible due to the low bond energy of metallic bonds compared to covalent bonds in salts. Barium has recently become a popular choice for high-fidelity trapped-ion experiments due to its favorable atomic structure. The larger number of slower moving atoms from barium metal demonstrates that metallic barium could be a much more promising atomic source for barium-based trapped-ion experiments, as the slower plume enables higher loading rates in surface-electrode ion trap systems. Finally, excess micromotion, caused by stray electric fields in RF traps, can lead to undesirable effects such as heating and frequency modulation of atomic transitions. This work evaluates the micromotion compensation capabilities of the Phoenix ion trap used in our system through numerical simulations of single ion trajectories. Through these simulations, it was determined that stray fields of Ex ≈ 3000 V/m, Ey ≈ 3800 V/m, and Ez ≈ 600 V/m can be effectively compensated for with the Phoenix ion trap. With typical stray electric fields in trapped-ion systems ranging from tens to a few hundred V/m, this demonstrates that the Phoenix trap should be well capable of compensating any stray fields expected in our system.
The Dynamical States and Mass Accretion Histories of Galaxy Clusters in IllustrisTNG
(University of Waterloo, 2025-09-19) Reid, Rashaad
The concordance cosmological model describes the history and large-scale structure of the universe using a few key parameters. Two of these parameters, σ8 and Ωm, determine the clustering of matter due to the growth of density fluctuations in the early universe. Current constraints on these parameters measured from nearby large structures and from the early universe are in statistical tension. Our ability to resolve this tension is limited by the degeneracy between the parameters when measured from observations of nearby structure. Since galaxy clusters are the most massive gravitationally bound objects in the universe, their formation is sensitive to σ8 and Ωm. An improved understanding of the formation histories of galaxy clusters can break the measurement degeneracy, thus providing new insights into this tension in our cosmological model. Since the formation time scales of galaxy clusters are unobservable, we must use the structure of clusters to probe their formation histories. In this thesis, we relate the observable structural properties of galaxy clusters to the mass accretion histories of their surrounding dark matter halos in the IllustrisTNG cosmo- logical simulations. Structure formation in the universe is hierarchical, so recently formed galaxy clusters will have experienced recent mergers with other systems. We examine a set of structural properties that are related to the dynamical states of clusters as indications of recent mergers to relate the structures of clusters to their formation histories. Using the cluster formation history information that is available in IllustrisTNG, we classify clusters as dynamically relaxed or unrelaxed based on their structural properties and compare the mean mass accretion histories of the resulting groups. We establish in this work that the stellar mass asymmetry and magnitude gaps of galaxy clusters are readily observable structural parameters that most effectively predict the mass accretion histories of halos. By comparing the gravitational lensing profiles of dynamically relaxed and unrelaxed clusters classified using different structural parameters, we demonstrate that the stellar mass asymmetry most reliably distinguishes between halos in different dynamical states with different density profiles. We also show that line of sight galaxy projection does not significantly affect IllustrisTNG cluster samples and that differences between 3D-identified clusters and optically selected clusters can be accounted for with accurate cluster mass estimates. However, we find that the density profiles traced by the weak gravitational lensing around relaxed and unrelaxed clusters in IllustrisTNG simulations and DLIS x UNIONS observations are discrepant. The structural differences between the simulated and observed galaxy clusters will be further explored in future work to better relate this work’s findings to real astrophysical systems. Overall, we find through cosmological simulations that the structural properties of galaxy clusters can be used to effectively trace their mass accretion histories. The findings of this thesis establish which observable properties of clusters can be targeted in both observations and simulations to grant us insight into the formation histories of the largest structures in the universe.
Fluctuation-induced order and thermal transport in frustrated quantum magnets
(University of Waterloo, 2025-09-18) Hickey, Alexander
Order-by-disorder is a mechanism of "fluctuation-induced" ordering that occurs in many frustrated magnetic systems where magnetic moments, or spins, are subject to competing interactions. So far, this phenomenon has been discussed in systems where the quantum ground state is not a "classical" product state. In such a case, both thermal and quantum fluctuations act to lift the accidental classical degeneracy, raising the question of whether one mechanism of order-by-disorder is possible without the other. In this thesis, we present results exposing a novel route to order-by-disorder, one without quantum zero-point fluctuations, in the ferromagnetic pyrochlore Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We show that any collinear ferromagnetic state is an exact eigenstate even in the presence of the anisotropic DM interaction, while thermal fluctuations give rise to a preferred magnetization direction. Using linear spin wave theory, we find that the anisotropy appears at lowest order as a sub-leading term in the low-temperature expansion of the free energy. Our results thus show that the phenomenon of thermal order-by-disorder can, in principle, occur even in the absence of quantum zero-point fluctuations driving quantum order-by-disorder. By extending our calculations to non-linear spin wave theory, we find that the ferromagnetic ground state becomes unstable for a spin-1/2 system when the DM interaction is large. Next, we ask the question of how to adequately characterize order-by-disorder in real materials, and how to distinguish it from conventional energetic ordering. Currently, the only clear and universal signature that has been proposed is a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. Thus far, this temperature dependence of the pseudo-Goldstone gap has only been characterized in the classical limit. Here, we use non-linear spin wave theory to characterize the pseudo-Goldstone gap in quantum magnets at low temperature, to leading order in 1/S. Using exact sum-rules for the magnon spectral functions, we find that the gap exhibits a distinct power-law temperature dependence. We examine the implications of our results for several candidate materials. The final part of this thesis examines the thermodynamic and transport properties of the ferromagnetic pyrochlore Lu₂V₂O₇. Over the last decade, there has been immense interest in magnetic materials that host topologically non-trivial excitations. In ordered magnetic insulators, features analogous to those of topological insulators and semimetals can arise in the magnon band structure, and the associated Berry phases can manifest in observable heat and spin transport phenomena. This was unambiguously observed in Lu₂V₂O₇ in the form of a magnon thermal Hall signal, and proposed to arise from the DM interaction. A precise value of the DM interaction is not known, as the values obtained from fitting both thermal transport and inelastic neutron scattering data, as well as from density functional theory, are all mutually inconsistent. Motivated by this, we investigate the effect of additional symmetry allowed perturbations to the spin Hamiltonian of Lu₂V₂O₇ in an attempt to reconcile the different experimental probes of this material. We find that the thermal transport and neutron scattering measurements are consistent with the addition of a small second-nearest-neighbour DM interaction to the model. Conversely, we argue that existing specific heat measurements are inconsistent with neutron scattering experiments and cannot be reconciled with any additional exchange couplings to the bilinear spin-model in the perturbative regime. Our results motivate future thermal transport and specific heat measurements of this material.
Asymptotic Higher Spin Symmetries: Noether Realization & Algebraic Structure in Einstein-Yang-Mills Theory
(University of Waterloo, 2025-09-17) Cresto, Nicolas
This thesis deals with the phase space realization of asymptotic higher spin symmetries, in 4-dimensional asymptotically flat spacetimes. These symmetries live on the conformal null boundary, namely null infinity, and were first revealed few years ago via the study of conformally soft gluons and gravitons operator product expansions, in the context of celestial holography. Connections with twistor theory and phase space realization followed soon after. In the gravitational case for instance, these symmetries generalize the BMS algebra to include an infinite tower of symmetry generators constructed from tensors on the sphere of arbitrary high rank s. The bulk interpretation of these transformation parameters is still largely under investigation. Building on a first series of results on their canonical representation, we develop the necessary framework to define Noether charges for all degrees s. Importantly, we construct these charges out of a `holomorphic' asymptotic symplectic potential, such that we obtain an infinite collection of charges conserved in the absence of radiation. The classical symmetry is then realized non-perturbatively and non-linearly in the so-called holomorphic coupling constant, generalizing the perturbative linear and quadratic approach known so far. The infinitesimal action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts of null infinity. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic equations of motion in vacuum. We expose our results for Yang-Mills, General Relativity, and Einstein-Yang-Mills theories. This canonical analysis comes hand in hand with an in-depth study of the algebraic structure underlying the symmetry. We reveal several Lie algebroid and Lie algebra brackets, which connect the Carrollian, celestial and twistorial realizations. We show that these brackets are a deformation of the soft celestial algebra, where the deformation parameters are the radiative asymptotic data. On the one hand they allow us to define the symmetry algebra at non-radiative cuts of null infinity, for arbitrary values of the asymptotic shear and gauge potential. On the other hand, we can accommodate for radiation using the algebroid framework. For the specific case of non-abelian gauge theory, we also investigate how the asymptotic expansion around null infinity of the full Yang-Mills equations of motion in vacuum can be recast in terms of the higher spin charge aspects. Since the analysis of higher spin symmetries is for now inherent to a truncation of the latter equations of motion, this paves the way towards the understanding of the relevance of these symmetries in the full theory.
Statistical Mechanics of Finite Length Semiflexible Wormlike Polymers
(University of Waterloo, 2025-09-03) Andersen, Nigel
The wormlike chain is a fundamental model in polymer physics used for describing the statistics of semiflexible polymers. It is a general model applicable to many polymers, with double-stranded DNA being a notable example. Previous theoretical work has focused on long polymers, where subtle differences in the choice of statistical ensemble are not relevant. This worked well in explaining early data on polymer stretching, but as more modern techniques have allowed for the stretching of shorter, more rodlike polymers, finite length ensemble effects have become visible in experimental measurements and computer simulations. Here, these effects are computed, and a full picture of wormlike chain statistical mechanics is presented. The new results are compared against several decades of polymer stretching literature, and are found to describe previously unexplained behaviour. Finally, the broad use of the model is demonstrated by applying it to DNA wrapped carbon nanotubes, a system that requires considering polymer flexibility, and predicting the pitch of the helical structure formed by these complexes.
Characterization of prostate tumor spheroid growth and response to treatment using dynamic optical coherence tomography
(University of Waterloo, 2025-08-18) Swanson, Steph
Prostate cancer, the most prevalent cancer in North American men, is often treated with radiation and in the case of advanced disease, with the first-line chemotherapeutic docetaxel (DTX). The use of in vitro cell culture as a model for in vivo patient tumors has been instrumental in understanding the cancer biology underpinning tumor development, progression, and treatment. Conventionally, in vitro cells were cultured as 2D monolayers on hard, flat surfaces. However, it has become well understood in the last half-century that the behavior of in vivo tumors is better replicated by small 3D aggregates of in vitro cancer cells called tumor spheroids. While cells proliferate along the spheroid periphery, the center of the spheroid succumbs to starvation and waste build up. In between forms an intermediate layer of hypoxic and non-proliferative quiescent cells: two characteristics associated with treatment resistance. Despite the physiological pertinence of spheroid culture, its 3D nature challenges conventional biological methods. Moreover, cell culture geometry influences cell behavior not only during treatment, but in post-treatment recovery and throughout measurement as well. The clonogenic assay is a gold standard method for quantifying cell survival following treatment; however, it requires spheroids to be disaggregated and cultured in 2D for colony formation, which alters the cellular response. Proliferation assays quantify cellular activity inside intact spheroids, but similarly lack spatial resolution. Although fluorescence microscopy (FM) enables spatially resolved spheroid evaluation, it remains largely qualitative rather than quantitative. Proliferation assays and FM also require the addition of exogenous agents that are invasive to the sample and struggle to penetrate large spheroids. Alternatively, optical coherence tomography (OCT) enables non-invasive, high-speed, volumetric imaging of biological tissues with cellular resolution. Analysis of temporal OCT intensity fluctuations generates dynamic OCT (dOCT) images that can provide a quantitative and spatially resolved measurement of cellular activity throughout the spheroid. Nevertheless, investigating treatment response in spheroids is known to be tedious and time consuming, and some questions of interest cannot be accessed experimentally with adequate accuracy. As such, mathematical in silico models of spheroids have become increasingly prevalent. The heterogeneity inherent to in vivo tumors and in vitro spheroids is recapitulated by discrete in silico methods like agent-based modeling (ABM). These methods simulate each cancer cell as an individual “agent” that responds to neighboring cells, nutrients, drugs, and other components of its local environment. In particular, the cellular Potts model (CPM) is a form of ABM with phenomenological utility, given adequate validation to experimental observations. As such, it can describe, visualize, interpolate, and potentially even extrapolate experimental data to guide future experiments. This dissertation investigated and validated emerging and under-used in vitro tools for characterizing prostate tumor spheroid growth and response to treatment with radiation and DTX. First, I created a semi-automated masking process to isolate spheroids from volumetric OCT images for high resolution morphological analysis. For analysis of dynamic motion, I generated dOCT images using a frequency banding method that had only been previously subject to qualitative evaluation. Then, I developed a technique to quantify cellular activity in volumetric dOCT images of masked spheroids. Visual and quantitative comparison of live and formaldehyde-fixed spheroids imaged with dOCT and FM confirmed that dynamic motion measured with the dOCT method was associated with cellular activity. To mitigate influences unrelated to cellular activity, the average measurement of formaldehyde-fixed spheroids was subtracted from quantitative dOCT measurement as background. Post-treatment recovery of prostate tumor spheroids exposed to DTX was investigated with repeated measurement via Alamar Blue (AB) proliferation assay and longitudinal observation of clonogenic assay colony formation. Excellent agreement was observed between the quantitative dOCT method and AB proliferation assay over two weeks of longitudinal spheroid growth. Volumetric morphological analysis supported the measured cellular activity trends. However, fixation-subtraction could not be performed in a spatially sensitive manner and the dOCT images failed to resolve the longitudinal formation of a necrotic spheroid core that was observed via FM. Nonetheless, dOCT images and quantification of spheroids post-radiation demonstrated good agreement with FM and AB, respectively. Spheroids treated with radiation and DTX demonstrated better survival compared to monolayer culture. Monolayer culture treated with low dose DTX demonstrated higher post-treatment cellular activity and faster colony formation, but clonogenic survival remained lower than the untreated control. This effect was also observed in spheroids, albeit to a lesser extent. Experimental observations were probed with novel in silico CPMs of prostate tumor spheroid treatment. This thesis serves as a step towards validating emerging and under-used in vitro tools for spheroid evaluation in well-studied conventional cancer treatments. Once validated, these in vitro tools are particularly well suited for discovery and testing of novel targeted cancer treatments since spheroid protein and gene expressions are more physiologically representative than monolayer culture.
Quantum Error Correction and Quantum Metrology with Non-Markovian Noise
(University of Waterloo, 2025-08-12) Mann, Zachary
Quantum technologies have the potential to solve many important problems across science and industry. An important example is quantum computation. Quantum simulators promise to better model chemistry. Further, Shor’s factoring algorithm solves a problem in exponentially less time than what it would take now on our classical computers. This has led many to believe that quantum computers could bring exponential speedups to other difficult, real-world problems, such as optimization. Another example is quantum sensing, where quantum mechanical effects can be leveraged to increase measurement precision beyond the classical state of the art. This has many applications in both fundamental science, such as the LIGO experiment, and in industry, such as Nitrogen vacancy magnetometers. For these quantum technologies to reach their full potential, however, the barrier of noise must be overcome. Quantum effects usually live at very small system sizes or very cold temperatures, making them extra sensitive to thermal noise or small perturbations of the environment. A proposed solution to this problem, for both computation and sensing, is to use quantum error correction. Quantum error correction encodes a few quantum degrees of freedom into many physical degrees of freedom, building in redundancy. This redundancy allows for the detection and correction of unwanted errors in our protocol. Most of the literature on quantum error correction focuses on Markovian noise models, i.e., models where the noise is not temporally correlated. The temporally correlated, or non-Markovian, regime remains relatively unexplored. In this thesis, we explore quantum error correction for non-Markovian noise models. We first present a few of the many definitions and models for quantum non-Markovian phenomena present in the literature. We then generalize the Knill-Laflamme quantum error conditions to the hidden Markov model, an experimentally motivated model of non-Markovian noise. These conditions allow one to guarantee that a quantum error-correcting code will still do its job for more realistic noise models. Finally, we apply our notion of non-Markovian error correction to quantum sensing. We generalize previous Markovian results and derive conditions for guaranteeing Heisenberg limited precision scaling in the presence of temporally correlated noise using quantum error correction. The Heisenberg limit is the fundamental precision limit allowed by quantum mechanics for parameter estimation in a physical system. We also study the next-best achievable precision scaling when the Heisenberg limit is unattainable.
Quantum Monte Carlo Simulations of Rydberg Atom Arrays
(University of Waterloo, 2025-07-07) Merali, Ejaaz
Rydberg atom arrays form a promising platform for quantum computation. Through their strong, long-range interaction, they are able to encode various difficult combinatorial problems, as well as hosting a plethora of intriguing physical phenomena. In this thesis, we develop and apply a Stochastic Series Expansion Quantum Monte Carlo method to simulate Rydberg systems at zero-temperature and above. We then apply this simulation method alongside variational models to verify correctness of both methods. The data produced from the simulations is also used to train Neural Network wavefunctions, which we find are effectively able to grasp some of the physics of the Rydberg atom array on a square lattice.
A Machine Learning Model for Trapped-ion State Classification
(University of Waterloo, 2025-05-14) Balaniuk, Severyn
Academia and industry have been working to build a quantum computer that is able to perform certain tasks significantly better than classical computers. This thesis focuses on improving a trapped-ion-based approach to quantum computing. This platform has advanced significantly over the last 10 years, but there are numerous issues we need to resolve to make this architecture scalable. We consider experiments that use a high-sensitivity photon detection module as the readout tool. This setup lets us see qubit measurement outcomes as a fluorescent signal on a digital camera. This thesis addresses the problem of classifying fluorescence states for experimental systems of up to four ions, representing them as binary sequences. Our model hopefully will be able to classify systems with 8, 16, and 32 ions, allowing for further application of this methodology as quantum computers grow in scale. Our datasets are mainly unlabelled, which is the biggest challenge for training an accurate machine learning (ML) model. Nevertheless, we showed a significant improvement in classification accuracy with reduced bias over legacy models on unlabelled data containing mixed states of a four-ion system. We tested different machine learning architectures like feed-forward neural network (FFNN), convolutional neural networks (CNN), and semi-supervised learning to evaluate their efficiency for our specific dataset and tested their performance. In addition, we also developed and improved our own FFNN architecture with custom loss functions.
Towards Optical Simulation of Topological Phenomena with Ring Resonators
(University of Waterloo, 2025-04-30) Kuchhal, Bharat
In recent years, there has been a growing interest in synthetic dimensions. Unlike physical dimensions where one is restricted with three possible dimensions, one can tailor a lattice system with several higher order dimensions even with a lower-order physical system. In this thesis, we will explore, both theoretically and experimentally, how equidistant frequency modes in a resonator—specifically a ring resonator—can be used as a synthetic dimension. In this respect, we will first explore basics of resonators by reviewing a Fabry Perot resonator and developing a coupled-mode theory to understand its transmission and reflection spectrum. We will then expand and develop a coupled-mode theory for the case of a ring resonator, and explore experimental results for a basic fiber-beam splitter based ring resonator. Next, we will modify the ring resonator with a few off the shelf fiber optic components like a Dense Division Wavelength Multiplexing filter, a fiber electro-optic modulator, and an optical amplifier, and see how they transform the transmission characteristics. Lastly, we will modulate the ring resonator at the same frequency as the free-spectral range of the resonator to couple the modes to observe a band structure in the reciprocal space, much like atoms in a periodic solid-state crystal coupled via Coulomb interactions lead to energy bands in the conjugate momentum space. For this purpose, we will develop a coupled-mode theory for a ring resonator modulated by a phase modulator, look at some theoretical results for symmetric and asymmetric band structures, and observe some experimental results for the symmetric case. Thus, we highlight the potential of fiber ring resonators as versatile platforms for optical simulation of topological systems. Further, the ability to replicate higher-dimensional phenomena using frequency modes opens new pathways for investigating exotic physical behaviors, such as non-Hermitian systems and synthetic magnetic fields, in compact and experimentally accessible setups.
A Multi-Phase Analysis of Gas Dynamics and Perturbations in the Galaxy Cluster Cores
(University of Waterloo, 2025-02-14) Li, Muzi; McNamara, Brian
This thesis provides a detailed analysis of gas kinematics and their interactions across various phases within galaxy cluster cores. It examines the processes that generate gas perturbations and the factors that contribute to the thermal stability of the intracluster medium (ICM). A focus is placed on exploring the origins of multi-phase gas and the mechanisms—particularly AGN feedback—that either couple or decouple their motions. Radio-mechanical AGN feedback is identified as one of the most promising heating mechanisms that prevent the cooling of gas. However, the debate on the details of the heating transport processes has remained open. The atmospheres of 5 cool-core clusters, Abell 2029, Abell 2107, Abell 2151, RBS0533 and RBS0540, have short central cooling times but little evidence of cold gas, and jet-inflated bubbles. The amplitudes of gas density fluctuations were measured using a new statistical analysis of X-ray surface brightness fluctuations within the cool cores of these ‘spoil’ clusters in Chapter 2. The derived velocities of gas motions, typically around 100 - 200 km/s, are comparable to those in atmospheres around central galaxies experiencing energetic feedback, such as in the Perseus Cluster, and align well with the turbulent velocities expected in the ICM. Regardless of the mechanisms driving these perturbations, turbulent heating appears sufficient to counteract radiative losses in four of the five spoiler cluster cores. We thus suggest that other mechanisms, such as gas sloshing, may be responsible for generating turbulence, offering a plausible solution to suppress cooling in these structureless atmospheres. Multiphase filaments, key byproducts of AGN feedback, are frequently observed near central galaxies, with their morphologies and kinematics closely linked to bubbles. In Chapter 3, we analyzed the velocity structure functions (VSFs) of warm ionized gas and cold molecular gas, identified through [OII] emission and CO emissions observed by the Keck Cosmic Web Imager (KCWI) and the Atacama Large Millimeter/submillimeter Array (ALMA), respectively, in four clusters: Abell 1835, PKS 0745-191, Abell 262, and RXJ0820.9+0752. Excluding Abell 262, where gas forms a circumnuclear disk, the remaining clusters exhibit VSFs steeper than the Kolmogorov slope. The VSFs of CO and [OII] in RXJ0820 and Abell 262 show close alignment, whereas in PKS 0745 and Abell 1835, were differentiated across most scales, likely due to the churning caused by the radio-AGN. The large-scale consistency in Abell 1835 and RXJ0820, together with scale-dependent velocity amplitudes of the hot atmospheres obtained from Chandra X-ray data, may support the idea of cold gas condensation from the hot atmospheres. X-ray observations have previously been constrained by low energy resolution, which has impeded direct measurements of velocity fields in galaxy clusters. However, the recent release of initial data from the X-ray Imaging and Spectroscopy Mission (XRISM) provides a non-dispersive energy resolution of about 5 eV, facilitating the measurement of line broadening and shifts. In Chapter 4 of this thesis, I detail my contributions to calibrating the optical blocking filters for XRISM using synchrotron beamlines at the Canadian Light Source (CLS) and Advanced Light Source (ALS) prior to its launch, and I discuss the model-based estimation of the parameters of the calibrated filters. This capability for direct measurement of plasma velocities is expected to greatly improve our understanding of the ICM dynamics with high accuracy.
Investigating Abundances in Galaxy Clusters and Gas Motions in M87 using XRISM
(University of Waterloo, 2025-01-24) Dizdar, Neo; McNamara, Brian
Galaxy clusters are the forefront of extragalactic diffuse X-ray astrophysics, yet there are still many questions about their formation and evolution. The creation of XRISM, a new X-ray imaging and spectroscopy mission, will study the metal abundance history of clusters and the conversion of jet energy into atmospheric kinetic energy. XRISM’s payload contains an instrument with the highest spectral resolution (5 eV) in the field of X-ray astronomy so far. With this resolution, we observed metal abundances and the broadening of metal lines through turbulent motions in the intracluster medium. In this thesis I present the conversion of data from the Chandra X-ray Observatory to XRISM’s high-resolution format. This includes the preparation and selection of clusters in Chandra, simulating selected clusters for XRISM and applying for proposals. Finally, we extracted abundance and velocity information from the Virgo cluster’s early XRISM data.
On the Initial Boundary Value Problem in Numerical Relativity
(University of Waterloo, 2025-01-23) Dailey, Conner; Afshordi, Niayesh; Schnetter, Erik
The principal goal of this thesis is to properly understand, characterize, and numerically implement initial boundary value problems in numerical relativity. Throughout the history of solving Einstein's field equations on computers, boundaries have been mostly dealt with in an approximate way. For example, boundaries might be placed far away from strongly gravitating sources, where approximations like linearized gravity are valid. It has become necessary however to place boundaries in the strong gravity regime of a dynamical spacetime to model complicated and interesting physics, which necessitates a complete understanding of the initial boundary value problem of Einstein's field equations. One motivation for this comes from a need to simulate black hole echoes. In classical general relativity, black holes are perfectly absorbing objects, where the mass of radially incoming wavepackets of matter or gravitational waves is absorbed by the black hole. Thus conclusive evidence of modifications to general relativity, such as quantum gravity, could include partial reflections of radially incoming wavepackets, called black hole echoes. To properly understand the modifications this would bring to detectable gravitational wave signals, we require simulations where reflecting boundary conditions are imposed close to the horizon of a black hole. Another motivation comes from recent advances in Cauchy characteristic matching, which combines state of the art numerical techniques to obtain physically accurate gravitational waveforms from simulations. This can allow numerical relativists to dramatically save on the computational cost of black hole merger simulations, but only if boundaries can be placed in the strong gravity regime. This thesis presents advances in simulating initial boundary value problems in numerical relativity. Starting with spherical symmetry, a framework for reflecting a scalar field in a fully dynamical spacetime is developed and implemented numerically using the Einstein-Christoffel formulation. The evolution of a wave packet and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole, is studied. Next, this approach is generalized to spacetimes with no symmetries and implemented numerically using the generalized harmonic formulation. The evolution equations are cast into a summation by parts scheme, which seats the numerical method closer to a class of provably numerically stable systems. State of the art numerical methods are demonstrated, including an embedded boundary numerical method that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of these frameworks, the evolution of gravitational wave scattering off of a boundary either inside or just outside the horizon of a black hole, is studied. Finally, a boundary condition framework designed to control quasi-local energy flux is proposed motivated by examples from electromagnetism.
Studies on the 1/f noise in Shunted Josephson Junctions and Effective Masses in 2DHG GaAs Hall Bars
(University of Waterloo, 2025-01-22) Coschizza, Andree; Kycia, Jan
Two projects are presented with the motivation of improving materials and devices for superconducting and semiconducting qubit applications. The first project focuses on quantifying the 1/f noise in SIS Josephson junctions using a dc SQUID. The current-voltage characteristics of two junctions are measured and the degree of thermal rounding is analyzed as a function of temperature. The current-voltage characteristics are then used to compute the voltage bias dependence of both the 1/f and white noise of the junction. Finally, the temperature dependence of the 1/f noise is investigated and found to exhibit a linear relationship within the region of 100mK-4.5K. This is then compared to similar systems in literature. The second project explores a GaAs/AlGaAs 2DHG system using quantum Hall effect measurements. The mobility and charge carrier density dependence is calculated, and an experiment is conducted to investigate their dependence on highly negative top gates. It is discovered that the mobility-density curve increases as the top gate is pushed to more negative values. Furthermore, the spin-orbit interaction is parameterized and compared to previously measured samples. Finally, the band structure of GaAs/AlGaAs holes is discussed in reference to the observed Shubnikov-de Haas oscillations. The effective mass corresponding to the light heavy hole subband is measured using the Ando, Fowler, and Stern equation at low magnetic field oscillations.
Time-resolved and equilibrium resonant X-ray studies of nematicity in cuprate superconductors
(University of Waterloo, 2025-01-16) Gupta, Naman Kumar; Hawthorn, David
Attracting four decades of experimental and theoretical investigations since the discovery of high-temperature superconductivity, cuprates have become an essential benchmark for the exploration of intertwined electronic symmetry-breaking phases such as superconductivity, magnetism, nematicity, charge or spin density wave order in strongly correlated systems. Understanding how these phases are intertwined is of general and fundamental interest to a wide range of quantum materials. This doctoral work employs the element- and orbital-specific sensitivity of time-resolved and equilibrium resonant X-ray scattering to investigate electronic nematicity and charge density wave (CDW) order in cuprates. By probing their responses to photoexcitation using ultrafast laser pump-probe setups, varying hole doping levels, and applying compressive uniaxial stress, this thesis attempts to disentangle, understand, and manipulate intertwined phases in stripe-ordered cuprates.
Neurovascular Coupling in healthy human retina evaluated with Optical Coherence Tomography
(University of Waterloo, 2024-12-21) Dhaliwal, Khushmeet; Bizheva, Kostadinka
Retinal neurodegenerative diseases such as glaucoma, age-related macular degeneration (AMD), diabetic retinopathy, and retinitis pigmentosa affect millions of people worldwide and pose a significant burden on public health and the economy. Glaucoma, impacting approximately 80 million people globally, is a leading cause of irreversible blindness. In 2019, an estimated 19.8 million Americans (12.6%) were living with AMD, of which about 1.49 million people faced vision-threatening conditions. An estimated 9.6 million people were living with diabetic retinopathy in 2021, with about 1.84 million of them experiencing vision-threatening stages. In the United States alone, vision impairments- including those resulting from these retinal diseases- cost an estimated $139 billion annually. Retinal neurodegenerative diseases not only cause progressive damage to the retinal morphology and vascular network, but also cause acute and transient metabolic, physiological, and blood flow changes at the early stages of the disease development which become permanent and chronic at the advanced stages of the disease. Neurovascular Coupling (NVC) refers to the transient vasodilation and increased retinal blood flow resulting from the increased metabolic activity of retinal neurons in response to visual stimulation. Over the past few decades, a range of imaging techniques from clinical ophthalmoscope and confocal microscopy to adaptive optics scanning laser ophthalmoscope and optical coherence tomography (OCT) have been used ex vivo and in vivo to study components of the neurovascular coupling and its underlying mechanisms. Techniques such as Laser Doppler Velocimetry, Optical Coherence Tomography Angiography (OCTA), and Doppler Optical Coherence Tomography (D-OCT) have been used to observe the vascular responses of the retina caused by visual stimulation. Additionally, Electroretinography (ERG) has been widely used in clinical settings to evaluate the electrical activity of the neuronal retina. More recently, an optical equivalent to ERG, Optoretinography (ORG) was developed and OCT technology, imaging protocols, and image processing algorithms were designed to conduct OCT-based ORG studies in the human and animal retina. However, most of the Doppler OCT, OCTA, and ORG studies have examined components of the neurovascular coupling separately, potentially overlooking the dynamic interactions and comprehensive responses inherent in neurovascular coupling. OCT, which acquires simultaneously both intensity and phase information, is particularly well-suited for investigating neurovascular coupling in the retina, as it enables a completely non-invasive approach for simultaneous monitoring of retinal blood flow dynamics and neuronal responses. The integration of a commercial ERG system with a research-grade OCT modality adds further value by offering easy control of the visual stimulus, use of clinically established ERG protocols designed to elicit responses from specific types of retinal neuronal cells, and using the ERG recordings to validate the visually-evoked neuronal responses. The main objectives of this PhD thesis were: 1. To develop a combined OCT+ERG imaging system to conduct in vivo and simultaneously morphological and functional imaging that can be utilized for investigating neurovascular coupling in the human retina. 2. To evaluate the performance and capabilities of the OCT+ERG system, imaging protocols, and image processing algorithms by conducting a pilot study on healthy human subjects. 3. To utilize the OCT+ERG technology to explore the neurovascular coupling mechanisms in the healthy human retina by extracting vascular and neuronal responses from different retinal layers simultaneously. 4. To examine the effects of different wavelengths and flicker frequencies on the dynamic retinal blood flow changes evoked by visual stimulation, providing deeper insights into the mechanisms of neurovascular coupling. Results from this PhD research have been summarized in three manuscripts that are either under review or under preparation for submission. Therefore, this PhD thesis was prepared in such a way that individual manuscripts represent separate thesis chapters.
The Evolution of Halo Properties Through Binary Major Mergers
(University of Waterloo, 2024-10-17) Marchioni, Justin; Taylor, James
Galaxy clusters are massive, gravitationally bound objects composed of a large population of galaxies. Each of these galaxies occupies a dark matter halo and collectively the cluster has its own extended halo. Cluster halos can be described by many structural properties including their mass, concentration, shape, spin, and asymmetry. These properties, among others, can be used as proxies to constrain cosmology. The issue with galaxy clusters is that they are still assembling at the present-day. These clusters primarily grow through mergers, where smaller systems coalesce to form larger ones. If the mass ratio between the two merging components is sufficiently large (i.e. 3:1 or below), this is known as a major merger. The effect of major mergers is to significantly redistribute the matter distribution in the host system. This leads to pronounced fluctuations in the cluster's structural properties during the merger, making measurements of these properties hard to interpret. Therefore, accurately predicting how cluster properties vary during mergers is important in order to use them as a cosmological tool. In this thesis, we use simulations to study how the structure of remnant systems evolves during mergers. These simulations consider the merger of two isolated components, each represented by truncated Navarro-Frenk-White (NFW) profiles. We find that mergers produce oscillations in structural parameters for both the overall remnant and the host system. For example, the host halo's concentration experiences one of two types of responses to the satellite's motion depending primarily on the pericentric passage distance of the orbit. Given the simulation results, we present a semi-analytic model for the evolution of structure in remnant systems due to isolated, binary mergers. The model consists of two components, a treatment for the orbital evolution of the satellite and a prescription for changes in the host halo's potential. This second component is often neglected when modeling satellite orbits in minor mergers. Interestingly, we find that adding a host halo response model has little impact on the orbital evolution of the satellite and its mass loss. In contrast, this model must be incorporated in order to accurately predict how the remnant's structure changes after the satellite first passes pericentre. While our model generally works well at replicating the median concentration for the first two orbits, it is unable to recreate any of the remnant's anisotropy properties (i.e. shape, spin, and asymmetry). Overall, our results provide a framework for analyzing the response of cluster halo properties to mergers in more realistic scenarios.
Characterization and First Results of an Inverse Photoemission Spectrometer
(University of Waterloo, 2024-09-26) Bouliane, Michael; Hawthorn, David
This thesis discusses our efforts to characterize our home built inverse photoemission spectrometer. We review the relevant theoretical and practical considerations for the technique of inverse photoemssion spectroscopy. We then detail our efforts to characterize our low energy electron gun, presenting a method for determining the total current delivered by the beam using just a Faraday cup. Measurements of the beam’s profile are presented and are used to calculate the parallel momentum resolution of the beam. Equally important is the characterization of our photon detectors, which we show are operating in the proportional region with a minimal dark count rate. We ascertained a spectrometer energy resolution of 415(55) meV by performing inverse photoemission measurements on polycrystalline gold foil, single crystal Cu (111), and pyrolytic graphite. As a final demonstration of our spectrometer’s capabilities we provide a full unoccupied band mapping for pyrolytic graphite showing its ability to resolve dispersive electronic features in reciprocal space.

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