Quantum Physics Commons^™

Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou

Dissertations, Theses, and Capstone Projects

Atomic delocalization due to nuclear quantum effects (NQE) remains poorly understood in low-temperature liquids near the glass state and during vitrification. Many liquids can be described accurately by treating their nuclei as classical particles, but this approximation fails for light elements such as He and H₂, small hydrogen-containing molecules such as water, and systems in which zero-point motion or isotope-substitution effects are important. Developing a general thermodynamic and statistical-mechanical description of such liquids has been challenging. This dissertation extends the potential energy landscape (PEL) formalism, originally developed for classical liquids and glasses, to liquids that obey quantum mechanics and exhibit …

Simulation Of Quantum Walks For Secure Data Access Patterns, Arslan Ahmad Janjua

Theses and Dissertations

Quantum computing is revolutionizing computational science, offering fundamentally new approaches to information processing that surpass classical limitations. One of the most versatile and powerful tools in this emerging field is quantum walks. Quantum walks are quantum analogs of classical random walks that leverage superposition and interference to explore complex spaces efficiently.

This thesis will explore how discrete-time scattering quantum walks can be simulated and analyzed to investigate patterns of secure data access. By modeling quantum walks on a variety of graph structures and studying the dynamics of marked vertices, the project aims to demonstrate how quantum interference and graph topology …

Non-Perturbative Aspects Of Gauge Theories Through A Complex Parametrization, Antonina Maj

Dissertations, Theses, and Capstone Projects

This dissertation explores a complex matrix parametrization of four-dimensional non-Abelian gauge theories as a means of gaining analytical insights into (3+1)-dimensional QCD. The low-energy scale of non-Abelian gauge theories remains an elusive area of research even after decades of work. A key challenge lies in identifying physical, gauge-invariant degrees of freedom that are relevant to non-perturbative phenomena. In this dissertation we develop a complex parametrization of gauge fields on which gauge transformations act homogeneously, thereby enabling a manifestly gauge-invariant analytical formulation of the theory.

Chapter one constructs the complex gauge-invariant parametrization for gauge theories living on both complex projective space …

Quantum Entanglement Correlations In The Proton On The Light-Front, Eric Kolbusz

Dissertations, Theses, and Capstone Projects

In this work we gather results on information theory applied to proton tomography. We start by analyzing the quantum entanglement of momentum, spin-flavor, and color degrees of freedom (d.o.f.) in the leading valence-quark state of the proton on the light front using standard information theoretical tools, leveraging model wavefunctions by Brodsky and Schlumpf to obtain numerical predictions. Light-cone perturbation theory allows us to introduce the one-gluon correction in the sub-leading Fock state and study the entanglement of the gluonic d.o.f. We find weak entanglement in the spatial d.o.f. of the valence quarks, and significantly stronger entanglement in the analogous d.o.f. …

Nonlinear Diffusion, Hydrodynamic Cascades And Jamming In Kinetically Constrained Systems: Insights From Lattice Gas Models, Abhishek Raj

Dissertations, Theses, and Capstone Projects

This dissertation investigates non-linear diffusion processes and emergent dynamical phenomena in kinetically constrained lattice gases. Two central models are considered: a one-dimensional lattice gas exhibiting a diffusion cascade triggered by hydrodynamic nonlinearities and a triangular ladder exclusion model that undergoes a jamming transition. The former demonstrates stretched exponential decay consistent with non-perturbative long-time tails, while the latter illustrates how classical-quantum mappings yield insight into glassy dynamics and mobility constraints. Through a combination of numerical simulations, analytical perturbation theory, and mean-field approximations, the work uncovers mechanisms underlying anomalous transport, jamming transitions, and the breakdown of perturbative hydrodynamics.

Excitons And Polaritons In Two-Dimensional Materials Heterostructures - Applications As Qubits, Time Crystals, And Superfluids, Gabriel Pimenta Martins

Dissertations, Theses, and Capstone Projects

This dissertation is concerned with exploring the properties and applications of excitons and polaritons in two-dimensional (2D) materials and heterostructures. It focuses on their potential to form qubits, time crystals, and superfluids. The work is motivated by the unique electronic and optical properties of 2D materials—specifically, their ability to host strongly bound excitons and hybrid light-matter quasiparticles known as polaritons. By exploiting a combination of theoretical modeling and numerical simulations, this work examines the behavior of these quasiparticles under various physical conditions, including strain-induced pseudomagnetic fields, optical microcavities, and periodic external potentials.

The first part of this dissertation is devoted …

Theoretical Proof Of And Proposed Experimental Search For The Ground Triplet State Of A Wigner-Regime Two-Electron ‘Artificial Atom’ In A Magnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

It is experimentally established that there is no ground triplet state of the natural He atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artificial atom’ or a semiconductor quantum dot in a magnetic field, as described by the Schrödinger–Pauli equation, we provide theoretical proof of the existence of a ground triplet state by deriving an exact analytical correlated wave function solution to the equation. The state exists in the Wigner high-electron-correlation regime. We further explain that the solution satisfies all requisite symmetry and electron coalescence constraints of …

Quantum-Mechanical Definition Of The Classical Scalar Potential In Schrödinger-Pauli And Schrödinger Theory, Viraht Sahni

Publications and Research

According to the Bohr correspondence principle, the external temporal scalar potential in the classical equation of motion is replicated in quantum theory as a multiplicative operator. An equivalent quantum-mechanical definition of the scalar potential in Schrödinger-Pauli/Schrödinger theory is provided. The potential is a known universal functional of the wave function. At each instant of time, it is the work done in a conservative “classical” field representative of internal properties of the system: Pauli and Coulomb correlations, kinetic effects, the density, the Lorentz force, an internal magnetic component, and the current density response. The Hamiltonians are thus rewritten in a …

Shear Viscosity Of Quasi One-Dimensional Bec Tubes And Entanglement Negativity Conditions, Camilla Polvara

Dissertations, Theses, and Capstone Projects

Shear Viscosity of Quasi One-dimensional BEC Tubes

We consider layered Bose-Einstein condensates interacting via contact intra-condensate interacions and dipolar inter-condensate potentials, both of which dominate intercondensate tunneling (which we neglect for simplicity). For this system, we compute the normal modes, we study its localization properties by numerically computing the inverse participation ratio, and we compute the inter-tube shear viscosity.

Entanglement Negativity Conditions

This project explores bounds on entanglement negativity using operator inequalities, building on the results of [1]. We are looking for a way to quantify entanglement, as an alternative to calculating the full negativity, which would otherwise require the …

Quantics Tensor Trains: The Study Of A Continuous Lattice Model And Beyond, Aleix Bou Comas

Dissertations, Theses, and Capstone Projects

This four-chapter dissertation studies the efficient discretization of continuous variable functions with tensor train representation. The first chapter describes all the methodology used to discretize functions and store them efficiently. In this section, the algorithm tensor renormalization group is explained for self-containment purposes. The second chapter centers around the XY model. Quantics tensor trains are used to describe the transfer matrix of the model and compute one and two-dimensional quantities. The one dimensional magnitudes are compared to analytical results with an agreement close to machine precision. As for two dimensions, the analytical results cannot be computed. However, the critical temperature …

Development And Application Of Magnus Expansion Based Propagators For Problems In Spectroscopy And Quantum Dynamics, Taner M. Ture

Dissertations, Theses, and Capstone Projects

Stable and accurate numerical propagators of time-evolution equations in quantum mechanics are required to capture correct dynamical behavior, especially in the long time limit. Magnus expansion (ME) provides a general way to expand the real time propagator of a time dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Integrators are developed by truncating the ME and using explicit integration of Lagrange interpolation formulas for the time dependent Hamiltonian within each time interval. The derived approximations are studied in a numerical test and compared to other available expressions. The sixth order expression is applied to …

Exciton Dynamics, Interaction, And Transport In Monolayers Of Transition Metal Dichalcogenides, Saroj Chand

Dissertations, Theses, and Capstone Projects

Monolayers Transition metal dichalcogenides (TMDs) have attracted much attention in recent years due to their promising optical and electronic properties for applications in optoelectronic devices. The rich multivalley band structure and sizable spin-orbit coupling in monolayer TMDs result in several optically bright and dark excitonic states with different spin and valley configurations. In the proposed works, we have developed experimental techniques and theoretical models to study the dynamics, interactions, and transport of both dark and bright excitons.

In W-based monolayers of TMDs, the momentum dark exciton cannot typically recombine optically, but they represent the lowest excitonic state of the system …

Robust Zero Modes In Non-Hermitian Systems Without Global Symmetries, Jose D. H. Rivero, Courtney Fleming, Bingkun Qi, Liang Feng, Li Ge

Publications and Research

We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the “nucleus” that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured …

Dynamics Of Spin And Charge Of Color Centers In Diamond Under Cryogenic Conditions, Richard G. Monge

Dissertations, Theses, and Capstone Projects

Individual quantum systems in semiconductors are currently the most sought-after platform for applications in quantum science. Most notably, the nitrogen-vacancy (NV) center in diamond features a defect deep within the electronic bandgap, making it amenable for precise manipulation to help pave the way to perform fundamental quantum physics experimentation. The NV center also offers long coherence times and versatile spin-dependent fluorescent properties, making it an ideal candidate for a nanoscale magnetometer. Furthermore, multi-color excitation offers deterministic charge state manipulation. While ambient operation has been key to their appeal, bringing NVs to cryogenic conditions opens new opportunities for alternate forms of …

Nonlinear Processes In Room Temperature Exciton-Polaritons, Prathmesh Deshmukh

Dissertations, Theses, and Capstone Projects

Strong light-matter coupling in solid state systems is an intriguing process that allows one to exploit the advantages of both light and matter. In this context, microcavities have become essential platforms for studying the strong coupling regime, where hybrid light-matter states known as exciton-polaritons form, leading to enhanced light matter interaction, modified material properties, and novel quantum phenomena. In this thesis, we explore the phenomenology of exciton-polaritons in strained TMD microcavities, 2D perovskites, fluorescent proteins and organic dyes encompassing thermalization, polariton lasing, and the observation of nonlinear effects.

Transition metal dichalcogenides (TMDs) have emerged as a remarkable class of two- …

A Quantum Approach To Language Modeling, Constantijn Van Der Poel

Dissertations, Theses, and Capstone Projects

This dissertation consists of six chapters. . . Chapter 1: We introduce language modeling, outline the software used for this thesis, and discuss related work. Chapter 2: We will unpack the transition from classical to quantum probabilities, as well as motivate their use in building a model to understand language-like datasets. Chapter 3: We motivate the Motzkin dataset, the models we will be investigating, as well as the necessary algorithms to do calculations with them. Chapter 4: We investigate our models’ sensitivity to various hyperparameters. Chapter 5: We compare the performance and robustness of the models. Chapter 6: We conclude …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The “Quantal Newtonian” Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a “probability amplitude.” A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or “Quantal Newtonian” Laws obeyed by each electron. These Laws, derived from …

Control Of Nonlinear Properties Of Van Der Waals Materials, Rezlind Bushati

Dissertations, Theses, and Capstone Projects

Van der Waals materials are a broad class of materials that exhibit unique optoelectronic properties. They provide a rich playground for which they can be integrated into current on-chip devices due to their nanometer-scale size, and be utilized for studying fundamental physics. Strong coupling of emitters to microcavities provides many opportunities for new exotic physics through the formation of hybrid quasi-particles exciton-polaritons. This thesis
focuses on exploring and enhancing nonlinearity of van der Waals materials through strongly coupling to microcavities. By taking advantage of the stacking order of TMDs, we show intense second-harmonic generation from bulk, centrosymmetric TMD systems. In …

The 'Quantal Newtonian' First Law: A Complementary Perspective To The Stationary-State Quantum Theory Of Electrons, Viraht Sahni

Publications and Research

A complementary perspective to the Göttingen-Copenhagen interpretation of stationary-state quantum theory of electrons in an electromagnetic field is described. The perspective, derived from Schrödinger-Pauli theory, is that of the individual electron via its equation of motion or ‘Quantal Newtonian’ First Law. The Law is in terms of ‘classical’ fields experienced by each electron: the sum of the external and internal fields vanishes. The external field is a sum of the electrostatic and Lorentz fields. The internal field is a sum of fields’ representative of Pauli and Coulomb correlations; kinetic effects; electron density; and internal magnetic component. The energy is obtained …

Charge Transport And Spin Dynamics Of Color Centers In Diamond, Damon Daw

Dissertations, Theses, and Capstone Projects

Solid state defects in diamond are promising candidates for room temperature quantum information processors (1, 3, 5). Chief among these defects is the nitrogen vacancy center (‘NV center’ or ‘NV’). The NV has long coherence times (at 300K) and its state is easily initialized, manipulated and read out (5). However, the outstanding issue of entangling NV centers in a scalable fashion, at room temperature remains a challenge. This thesis presents experimental and theoretical work aimed at achieving this goal by developing the ‘flying qubit’ framework in (1). This method for remote entanglement utilizes a charge carrier (initialized into a definite …

Quark And Gluon Entanglement In The Proton On The Light Cone At Intermediate X, Adrian Dumitru, Eric Kolbusz

Publications and Research

In QCD with $N_c$ colors the antisymmetric valence quark color space singlet state $\sim \epsilon_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of the proton corresponds to the reduced density matrix $\rho_{ij}=(1/N_c) \delta_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, $\lambda_i=1/N_c$, the purity $\tr \rho^2 = 1/N_c$, and the von Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximal entanglement of color. On the other hand, for $N_c\to\infty$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field [E. Witten, Nucl. Phys. B160, 57 (1979)] where there is no entanglement of spatial degrees of …

Photonics Of Time-Varying Media, Emanuele Galiffi, Romain Tirole, Shixiong Yin, Huanan Li, Stefano Vezzoli, Paloma A. Huidobro, Mário G. Silveirinha, Riccardo Sapienza, Andrea Alù, J. B. Pendry

Advanced Science Research Center

Time-varying media have recently emerged as a new paradigm for wave manipulation, due to the synergy between the discovery of highly nonlinear materials, such as epsilon-near-zero materials, and the quest for wave applications, such as magnet-free nonreciprocity, multimode light shaping, and ultrafast switching. In this review, we provide a comprehensive discussion of the recent progress achieved with photonic metamaterials whose properties stem from their modulation in time. We review the basic concepts underpinning temporal switching and its relation with spatial scattering and deploy the resulting insight to review photonic time-crystals and their emergent research avenues, such as topological and non-Hermitian …

Moiré-Driven Topological Transitions And Extremeanisotropy In Elastic Metasurfaces, Simon Yves, Matheus Inguaggiato Nora Nora Rosa, Mohit Gupta, Massimo Ruzzene, Andrea Alù

Advanced Science Research Center

The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat-band superconductivity in twisted graphene bilayers, of higher-order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to …

Extractable Entanglement From A Euclidean Hourglass, Takanori Anegawa, Norihiro Iizuka, Daniel Kabat

Publications and Research

We previously proposed that entanglement across a planar surface can be obtained from the partition function on a Euclidean hourglass geometry. Here we extend the prescription to spherical entangling surfaces in conformal field theory. We use the prescription to evaluate log terms in the entropy of a conformal field theory in two dimensions, a conformally coupled scalar in four dimensions, and a Maxwell field in four dimensions. For Maxwell we reproduce the extractable entropy obtained by Soni and Trivedi. We take this as evidence that the hourglass prescription provides a Euclidean technique for evaluating extractable entropy in quantum field theory.

Two-Loop Four-Fermion Scattering Amplitude In Qed, R. Bonciani, A. Broggio, S. Di Vita, A. Ferroglia, M. K. Mandal, P. Mastrolia, L. Mattiazzi, A. Primo, J. Ronca, U. Schubert, W. J. Torres Bobadilla, F. Tramontano

Publications and Research

We present the first fully analytic evaluation of the transition amplitude for the scattering of a massless into a massive pair of fermions at the two-loop level in quantum electrodynamics. Our result is an essential ingredient for the determination of the electromagnetic coupling within scattering reactions, beyond the currently known accuracy, which has a crucial impact on the evaluation of the anomalous magnetic moment of the muon. It will allow, in particular, for a precise determination of the leading hadronic contribution to the (g − 2)_μ in the MUonE experiment at CERN, and therefore can be used to …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The 'Quantal Newtonian' Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a ‘probability amplitude’. A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper we present a new perspective on such determinism. The ideas are based on the equations of motion or ‘Quantal Newtonian’ Laws obeyed by each electron. These Laws, derived from the …

Wave Function Identity: A New Symmetry For 2-Electron Systems In An Electromagnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

Stationary-state Schrödinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schrödinger-Pauli theory Hamiltonian with a symmetrical binding potential, we report a new symmetry operation of the electronic coordinates. The symmetry operation is such that it leads to the equality of the transformed wave function to the wave function. This equality is referred to as the Wave Function Identity. The symmetry operation is a two-step process: an interchange of the spatial coordinates of the electrons whilst keeping their spin moments unchanged, followed by an inversion. The Identity …

Linear And Non Linear Properties Of Two-Dimensional Exciton-Polaritons, Mandeep Khatoniar

Dissertations, Theses, and Capstone Projects

Technology has been accelerating at breakneck speed since the first quantum revolution, an era that ushered transistors and lasers in the late 1940s and early 1960s. Both of these technologies relied on a matured understanding of quantum theories and since their inception has propelled innovation and development in various sectors like communications, metrology, and sensing. Optical technologies were thought to be the game changers in terms of logic and computing operations, with the elevator pitch being "computing at speed of light", a fundamental speed limit imposed by this universe’s legal system (a.k.a physics). However, it was soon realized that that …

Experimental Observation Of Topological Z2 Excitonpolaritons In Transition Metal Dichalcogenide Monolayers, Mengyao Li, Ivan Sinev, Fedor Benimetskiy, Tatyana Ivanova, Ekaterina Khestanova, Svetlana Kiriushechkina, Anton Vakulenko, Sriram Guddala, Maurice Skolnick, Vinod M. Menon, Dmitry Krizhanovskii, Andrea Alù, Anton Samusev, Alexander B. Khanikaev

Publications and Research

The rise of quantum science and technologies motivates photonics research to seek new platforms with strong light-matter interactions to facilitate quantum behaviors at moderate light intensities. Topological polaritons (TPs) offer an ideal platform in this context, with unique properties stemming from resilient topological states of light strongly coupled with matter. Here we explore polaritonic metasurfaces based on 2D transition metal dichalcogenides (TMDs) as a promising platform for topological polaritonics. We show that the strong coupling between topological photonic modes of the metasurface and excitons in TMDs yields a topological polaritonic Z₂ phase. We experimentally confirm the emergence of one-way …

The Exact Factorization Equations For One- And Two-Level Systems, Bart Rosenzweig

Theses and Dissertations

Exact Factorization is a framework for studying quantum many-body problems. This decomposes the wavefunctions of such systems into conditional and marginal components. We derive corresponding evolution equations for molecular systems whose conditional electronic subsystems are described by one or two Born-Oppenheimer levels and develop a program for their mathematical study.