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ItemDensity-Induced Spin-Nematic Squeezing in a Spin-1 Bose-Einstein Condensate(Georgia Institute of Technology, 2024-04-28) Barrios, MaryroseDensity or pressure modulation of materials is an important method for tuning and engineering interactions within materials studied in condensed matter systems. This tuning is often used to alter or modify the underlying properties of the material, leading to the crossing of a phase transition or enhanced chemical or mechanical properties. This thesis investigates the possibility of whether a similar approach might be employed in the study of ultracold atoms present within a spinor condensate. In our system we use the confining trap potential to modulate and increase the density of the system in such a way as to push the cloud of atoms from non-interacting to interacting, and across a quantum critical point. By crossing over into this new phase, we are able to perform a constant magnetic field quench to observe both spin mixing and spin-nematic squeezing. This allows us to achieve -8.4 ± 0.8 dB of squeezing and shows promise for future density-driven interactions.
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ItemUnraveling the Knot-so-Simple Behavior of Knitted Fabrics(Georgia Institute of Technology, 2024-04-27) Singal, KrishmaKnitted fabrics are a ubiquitous part of our day-to-day lives. Although we primarily interact with it through clothing, the programmable nature of knitted fabrics lends to its potential in a myriad of fields. Knitting is made by manipulating yarn, which is often inelastic, into a lattice of slipknots with emergent elastic properties. How the yarn is manipulated throughout the fabric, what stitches it forms and how they’re patterned, impacts the resultant fabric behavior under mechanical deformation. Traditionally, this elastic response of knitted fabrics is qualitatively determined, but this study works to systematically understand and quantify the programmable nature of knitted materials. We find that small scale changes in the topology of the yarn between stitches, the boundaries between stitches, have large scale impacts on the bulk fabric response. Not only on the stitch level, but the lengthscale of these boundaries further influences the fabric behavior. We probe the multi-scale behavior and application of knitting through several experimental studies: varying constituent yarn type composing the fabrics, comparing behaviors of classic periodic knitting patterns, exploring the impact of aperiodic patterned fabrics, and testing applications of knitting in biomimicry and biomechanics via known pattern composites.
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ItemDynamics and Transport in Strongly Correlated Quantum Magnets(Georgia Institute of Technology, 2024-04-24) Hakani, SamiThis dissertation discusses Raman dynamics and chiral orbital currents in strongly correlated quantum magnets. Such spin systems can host exotic quantum liquid phenomena including fractional excitations, emergent gauge fields, and novel particle statistics. In addition to broadening basic scientific knowledge, understanding the dynamics and transport of these magnetic systems can further technological applications in quantum computing and electronics. This is demonstrated by probing quantum liquid phenomena using Raman scattering on the spin-1/2 quantum liquid candidate Ba4Ir3O10. In a collaborative study, Raman scattering provides three signatures for fractional spinon excitations: (1) a broad spectral hump consistent with a continuum arising from 4-body scattering of Luttinger spinons, (2) strong phonon damping due to spin-phonon coupling due to spin-orbit interactions, and (3) the absence of (1) and (2) and the precipitation of magnetic order due to a 2% non-magnetic chemical substitution. Transport phenomena is studied in ferrimagnetic Mn3Si2Te6 which demonstrates colossal magnetoresistance in absence of magnetic polarization. In a second collaborative study, a crystallographic symmetry analysis demonstrates chiral orbital current patterns are consistent with experimental transport measurements. The demonstrated control of chiral orbital current enabled colossal magnetoresistance provides potential utility for future quantum technological applications. Finally, a novel effect in Raman dynamics is explored in the presence of crystalline topological defects. Even when such defects do not couple to the low energy Hamiltonian, it is shown that they can produce qualitatively new effects by coupling to electric field probes. Such effects rely on an underlying spinon liquid state, and they are not observed for magnetically ordered or gapped phases. Potential applications include using crystalline topological defects to modify response-theory operators independently of the Hamiltonian and thereby generate new probes of quantum phases.
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ItemModeling Ganymede's Interaction with the Jovian Magnetosphere: Ionospheric Outflow and the Juno PJ34 Flyby(Georgia Institute of Technology, 2024-04-04) Stahl, Aaron M.Using a hybrid model (kinetic ions, fluid electrons), we provide a three-dimensional model of Ganymede’s interaction with the Jovian magnetosphere and the moon’s ionospheric outflow. We also provide context for plasma and magnetic field observations from Juno's PJ34 flyby of Ganymede on 07 June 2021. Using five model configurations that successively increase the complexity of Ganymede’s atmosphere and ionosphere through the inclusion of additional particle species and ionization mechanisms, we examine the density and flow patterns of pick-up ions with small (H2+), intermediate (H2O+), and large (O2+) masses in Ganymede’s interaction region. The results are validated by comparing the modeled magnetic field and ion densities against time series from Juno’s magnetometer and plasma instruments. The major findings are: (a) Ganymede’s internal dipole dominated the magnetic field signature observed inside the moon’s magnetosphere, while plasma currents shaped the field perturbations within the “wake” region detected along the Jupiter-averted magnetopause. (b) Ganymede’s pick-up tail leaves a subtle, but clearly discernible imprint in the magnetic field downstream of the moon. (c) Heavy pick-up ions dominate ionospheric outflow and form a tail with steep outer boundaries. (d) During the Juno flyby, the position of Ganymede’s Jupiter-facing magnetopause varied in time due to Kelvin-Helmholtz waves traveling along the boundary layer. As such, the location of the Jupiter-facing magnetopause observed by Juno represents only a single snapshot of this time-dependent process. (e) Ionospheric hydrogen ions are partially generated outside of Ganymede’s magnetopause, forming a dilute H2+ corona that surrounds the moon’s magnetosphere. (f) Most H2O+ ions are produced at low latitudes where field lines are closed, resulting in a very dilute pick-up tail for this species.
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ItemExact coherent structures and non-universality in the direct cascade in two-dimensional turbulence(Georgia Institute of Technology, 2024-01-10) Zhigunov, DmitriyTurbulence is the most important problem in physics and applied mathematics, with applications ranging from astrophysics, to engineering, to plumbing, and more. Turbulent flows are often characterized by the presence of various cascades, which transport various quantities across length scales. This dissertation focuses on turbulence confined in two-dimensions, which has two cascades: an inverse (energy) cascade that moves energy towards increasingly larger scales, and a direct (enstrophy) cascade that moves the enstrophy towards smaller scales. The energy cascade leads to the formation of large-scale vortices, which often take up the largest length allowed by the domain. The first part of this dissertation flows focuses on the dynamics of these large scale vortices, where we find that these vortices behave for substantial time intervals like specific solutions of the Euler equation. These solutions are in many ways analogous to recurrent solutions of the Navier-Stokes equation which are often referred to as exact coherent structures. On the other hand, these solutions have a number of properties which distinguish them from their Navier-Stokes counterparts, such as the fact that they exist in continuous, multiparameter families. At the same time, the classical theory of the direct cascade by Kraichnan, Leith, and Batchelor fails to predict the proper scaling of the enstrophy spectrum found in numerical simulations and experiments. This discrepancy is often attributed to the presence of large-coherent vortices. We will provide a physically interpretable mechanism for the direct cascade that recovers KLB predictions in the absence of large-scale vortices, but leads to deviations in their presence. Finally, we return directly to the large-scale dynamics we explain in the first section, and investigate exactly how properties of the large-scale flow affect the scaling of the enstrophy spectrum.
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ItemAbstract and Physical Effects of Curvature on Dynamics of Extended Body Systems(Georgia Institute of Technology, 2023-12-07) Day, BrianThe presence of intrinsic curvature of an ambient space influences the dynamics of point particles moving through it as typically considered in applications of differential geometry in physical contexts, such as general relativity. We aim to utilize the mathematics of differential geometry to instead consider the collective curvature effects on extended body systems in some generic curved space. To this end we develop a mathematical framework which serves as the foundation of a general dynamics solver numerical toolkit in which users can simulate the dynamics of discrete extended body systems in generic curved spaces. Through analyzing the dynamics of such extended body systems we recognized a relationship between deformation of the body during its dynamics as a result of the ambient curvature. This led us to expand our mathematical model of extended bodies to include deformable bodies. We find that such deformable bodies can generate collective motion via deforming their body even in a ambient space lacking curvature. This is due to the presence of an abstract notion of curvature defined on the configuration space of the system via considering the system as being described by a mathematical object known as a fiber bundle. This revelation allows us to discuss the dynamics of such deformable control systems using the ideas of geometric mechanics. In particular, we consider recasting our system in a geometric mechanics framework to address the question of determining optimal controls of how to deform the system so as to minimize some cost function. This is based on considering the optimization problem as a variational problem whose solutions correspond to optimal controls of the system. We develop this variational approach into a numerical toolkit acting as the foundation of a more general purpose optimization toolkit for deformable control systems described by fibers bundles.
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ItemBiomolecules' conformational changes studied by simulations and enhanced sampling(Georgia Institute of Technology, 2023-11-17) Pang, Yui TikBiomolecules, ranging from small molecules like vitamins to proteins, play critical roles in sustaining cellular functions. Their functionality is closely tied to their ability to undergo conformational changes in response to environmental conditions or binding events. In drug design, understanding the conformational flexibility of small molecules is crucial. Small molecules can undergo conformational changes that affect their interactions with target proteins. This understanding is vital for predicting drug behavior and interactions in biological systems. Proteins, which are central to various biological processes, have intricate conformational dynamics. They can shift between various conformations to fulfill their functions, from subtle side chain rearrangements to extensive structural changes. Misfolded proteins can lead to diseases, making the study of protein conformational changes critical in both understanding biological processes and developing therapies. Molecular dynamics simulations offer a powerful tool for studying biomolecular dynamics. These simulations allow for precise control and measurement of various aspects of biomolecular systems, providing insights into their structural dynamics. However, some biological processes occur on long timescales, necessitating enhanced sampling techniques to accelerate simulations and capture rare events. In this thesis, we investigated three distinct biomolecular systems: capsid assembly modulator AT130, passenger domain of pertactin, and SARS-CoV-2 spike protein. Employing advanced simulation techniques and enhanced sampling methods, we delved into the intricate behaviors of these biomolecules, each representing a unique aspect of biological complexity. During this exploration, I also updated the open-source parameterization tool, Force Field Toolkit, to accommodate the novel sigma-hole particle (LP) introduced in CGenFF 4.0. Our research spanned a range of scales and complexities, showcasing the adaptability and relevance of simulations and enhanced sampling approaches in the study of diverse biological systems.
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ItemOn the Generalization of Shadowing to Fluid Turbulence: Practical Methods For Quantifying Dynamical Similarity(Georgia Institute of Technology, 2023-07-31) Pughe-Sanford, Joshua L.Chaos is an intrinsic property of many real world systems, impacting a number of today's open research questions. While many chaotic systems have known governing equations and are deterministically “solved,” we still lack a comprehensive framework for predicting, controlling, and simply making sense of such systems. And while recent advances in technology allow us to explore these systems through direct numerical simulation better than ever before, the need for an insightful theoretical framework is still very much alive. Such a framework exists in a subset of chaotic systems, known as Axiom A chaotic systems. As a result, Axiom A systems are understood quite well. However, the requirements for a system to be Axiom A are quite strict, and the overlap between systems that are Axiom A and those that are physically significant is quite small. A very important concept in Axiom A systems is the notion of shadowing, which allows the chaotic dynamics to be decomposed piecewise-in-time in terms of much easier to analyze solutions known as periodic orbits. Periodic orbits are solutions to the governing equations that, unlike chaos, repeat in time. Their compactness make periodic orbits very simple objects to manipulate, both numerically and theoretically. This decomposition ultimately results in a predictive theory of Axiom A systems both deterministically and statistically. In this dissertation, we seek to generalize the concept of shadowing to a broader class of (non Axiom A) chaotic systems, specifically, fluid turbulence. Although recent studies suggest that Exact Coherent Structures—e.g., repeating solutions to the Navier-Stokes equation—are descriptive of turbulence, it is an open question whether they are to turbulence what periodic orbits are to Axiom A chaos. Here, we propose a generalized method for quantifying shadowing and discuss the generalized nature of shadowing in turbulence. Our results suggest that an axiom A framework for chaos may be more generalizable than previously thought.
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ItemAchieving a Quantum Simulator in Ultracold Fermionic Systems(Georgia Institute of Technology, 2023-07-30) Xiong, FengReal world material systems often have properties with roots in quantum mechanics which we are interested in. Studying such systems by classical models is often unsuitable, being either ineffective or inefficient. The general approach is utilizing laser cooled and trapped atoms as quantum simulators. This thesis presents our study of ultracold quantum gases of Li-6, signifying our progress in building a quantum simulator and providing a platform for conducting quantum simulation experiments. First, we demonstrate the achievement of quantum degeneracy in the form of molecular Bose-Einstein condensates (mBECs) of Li-6 in its lowest and second lowest two hyperfine state pairs by an all-optical method. We employ mostly standard techniques, but also introduce several unique features in our hardware system. Then, by preparing a degenerate Fermi gas of Li-6 in a mixture of its second lowest two hyperfine states and measuring its spin susceptibility in the BEC-BCS crossover, we study the “pseudogap” effects and compare it to the high-Tc cuprates. We develop a novel radiofrequency method to map the mixture to an RF-dressed basis. Imbalances are created between thermally equilibrium RF-dressed states, from which the spin susceptibilities are extracted over the interaction strength-temperature phase diagram. The results of such measurements for gases in the strongly interacting regions are compared to a mean-field model, to the ideal Fermi gas model, and to experimental results from several other publications. Lastly, we implement a 1D optical lattice and tune the single particle dispersion relation through dynamically modulating the lattice by Floquet engineering. The driving signal is modulated through an IQ modulator fed to two AOMs. By loading a molecular BEC of Li-6 pairs into the shaken lattice, we achieve coupling between the first two energy bands resulting in a double-well dispersion. The major result of our observations is that the sample under the inverted dispersion bifurcates into two soliton-like peaks in the momentum space. While in the position space, a density corrugation is formed in the condensate, which is caused by the two bifurcated wave peaks with opposing momentum beginning to separate. We have not yet fully understood the mechanism behind this phenomenon. For now, we model the result semi-classically by the Gross-Pitaevskii equation, from which the numerical simulations match reasonably well with the experimental results.
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ItemPhysics-Inspired Machine Learning of Partial Differential Equations(Georgia Institute of Technology, 2023-07-30) Golden, Matthew RyanThis dissertation discusses the Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) algorithm, which is a technique for data-driven discovery of governing equations of physical systems. SPIDER combines knowledge of symmetries, physical constraints like locality, the weak formulation of differential equations, and sparse regression to construct mathematical models of spatially extended physical systems. SPIDER is a valuable tool in synthesizing scientific knowledge as demonstrated by its applications. First, libraries of terms are constructed using available physical fields. The symmetries of a system allow libraries to be projected into independently transforming spaces, known as irreducible representations. This breaks relations down into their indivisible parts; each minimal physical relation is learned independently to reduce implicit bias. A library of nonlinear functions is constructed for each irreducible representation of interest. Second, each library term is evaluated in the weak formulation. SPIDER is aimed at experimental systems with inherently noisy data making accurate estimation of derivatives difficult. The weak formulation solves this problem: library terms are integrated over spacetime domains with flexible weight functions. Integration by parts can avoid numerical differentiation in many situations and increases robustness to noise by orders of magnitude. Clever weight functions can remove discontinuities and even entirely remove unobserved fields from analysis. Third, a sparse regression algorithm can find parsimonious relations ranging from dominant balances to multi-scale quantitatively accurate relations. Applications to direct numerical simulation of 3D fluid turbulence and experimental 2D active nematic turbulence are presented. SPIDER recovered complete mathematical models of both systems. The active nematic system is of particular interest; SPIDER identified a 2D description contradicting widely accepted theoretical descriptions used for over a decade. SPIDER facilitated the discovery of a new physical constraint on the fluid flow.