This thesis is the result of work on two separate Bose-Einstein condensate (BEC) experiments. First, I describe several projects in the construction of an ultracold Er and Na mixture experiment (Er:Na experiment). These include the design and characterization of a high temperature induction oven for Er as well as the capture of Er atoms into a 2D magneto-optical trap (2D MOT). Together, the induction oven and 2D MOT constitute a novel, compact source of cold Er atoms. Additionally, the construction and characterization of high current magnetic field coils for a magnetic quadrupole trap (MQT) and Helmholtz coils for future Feshbach spectroscopy are detailed.

Second, I describe a series of experiments with spinor gases carried out on the JQI Na spinor apparatus. In the first experiment, I demonstrate the freezing of nonlinear spin mixing dynamics in a 23Na BEC using a microwave dressing. This technique can be used to preserve squeezing of a probe state in future metrological applications. The spinor phase of a frozen state evolves at an enhanced rate proportional an effective quadratic Zeeman shift, q, of the |F = 1, mF = 0⟩ energy level.

In the second experiment, I demonstrate a radio frequency (rf) atomic spin-1 Ramsey interferometer which can measure the effective q, and thereby the spinor phase precession rate of a frozen probe state. The interferometer can simultaneously measure the rf detuning and q, and I demonstrate that it can be operated in both resonant and off-resonant regimes, using differential phase modulation between the two Ramsey pulses. The spin-1 Ramsey interferometer therefore has distinct advan- tages over both rf and microwave Rabi spectroscopy which are alternative methods to measure the effective q.

Finally, I demonstrate theoretical grounds for spin squeezing in a cold spin-1 thermal gas. In particular, I derive a spin-1 Boltzmann transport equation for the Wigner phase space density operator without recourse to Hartree-Fock theory. I then apply three different theoretical paradigms to model an experimental observation of classical relative number squeezing in a cold spin-1 thermal gas of Na: a simplified undepleted pump model which I solved analytically, a semiclassical quasiprobability distribution (QPD) numerical method, and numerical solution of the Schro ̈dinger equation using Fock states.

The nature of dark matter is a crucial problem for both cosmology and particle physics. The weakly interactive massive particle (WIMP) is one of the top dark matter candidates searched for decades because of the so-called ‘WIMP-miracle’. Dual phase liquid xenon time projection chambers (LXeTPC) have led the most sensitive searches on the GeV-scale spin-independent WIMP-nucleus scattering cross section for years because of the strong background suppression and scalability. With 3.7 tonne liquid xenon in the sensitive region of the LXeTPC, the Particle AND Astrophysical Xenon (PandaX) collaboration is now running PandaX-4T experiment at the B2 Hall of China Jinping Underground Laboratory after the PandaX-II experiment. The strongest limit back to the release time was published with the 0.63 tonne·year exposure on the standard thermal WIMP search with a lowest excluded cross section (90% C.L.) of 3.8 × 10^(−47) cm^2 at a dark matter mass of 40 GeV/c^2.

In this dissertation, I discuss research and developments correlated to PandaX experiments. I present the whole procedure of Rb-83/Kr-83m calibration in the PandaX-II detector from sources production with 3.4/20 MeV protons bombardment on natural krypton to the data analysis after injection into the PandaX-II detector, which becomes crucial for the increasingly larger detectors. With the Kr-83m events, the horizontal position construction algorithms in PandaX-II are improved, which is important to fully take advantage of the self-shielding ability of xenon, determining the fiducial volume directly related to the exposure. Moreover, I discuss the procedure of the profile likelihood ratio analysis to set the limits and sensitivities, where probability distribution functions are prepared with reweighting Monte Carlo to handle the systematic uncertainties in the detector response modeling more robustly. The methodology is applied on the spin-independent WIMP search to prove consistency with the template morphing method. Then, I conduct a search on electronic absorption of sub-MeV fermionic dark matter which shares similarities with sterile neutrino dark matter. Such dark matter with a 60 keV/c^2 mass can explain the low-energy ER excess reported by XENON1T collaboration, but is only marginally allowed by our constraints.

This dissertation presents experimental research into the nonlinear propagation of Terawatt class lasers in air over 1—40 m. Lasers of this power undergo filamentation; Kerr lensing in air leads to self-focusing which is arrested by photoionization. For λ = 800 nm the dynamic balance of self-focusing and plasma defocusing generates beams with a ~100 µm transverse size that is maintained over many meters. Heating from plasma recombination and relaxation of molecular rotations generates a single cycle acoustic wave and thermal profile which dissipates on the millisecond timescale.

We first use a novel array of synchronized microphones to observe extended air heating from a single laser shot. Single shot measurements allow the observation of air turbulence effects highlighting their importance even in a controlled lab environment. Armed with new knowledge about air heating we demonstrate filament applications for fog clearing, triggering high voltage spark gaps, and generating air waveguides. We show that both fog clearing and high voltage spark gap triggering are possible with air heating driven primarily by resonantly excited rotational states of air molecules rather than plasma. By utilizing beam shaping and multi-filamentation we demonstrate long range air waveguides limited only by the 40 m length of our test range.

Majorana zero modes (MZMs) can be fault-tolerant topological qubits due to their topological protection property and non-Abelian statistics. Over the last two decades, a deluge of theoretical predictions and experimental observations has been actively ongoing in the hope of implementing topological quantum computation upon MZMs. Among several solid-state systems, the most promising platform to realize MZMs is the one-dimensional semiconductor-superconductor nanowire (called ``Majorana nanowire'' in short), which is the focused system in this thesis. It is fundamental to identify MZMs as qubits to construct topological quantum computers. Therefore, the signatures of MZMs become highly crucial for verification. However, the earlier theoretical works demonstrate that topologically trivial Andreev bound states (ABSs) can mimic the hallmarks of MZMs in various aspects but do not carry topological properties. As a result, distinguishing MZMs from ABSs becomes significantly pivotal in the study of Majorana nanowire.

One of the signatures the author studied is the robustness of the quantized zero-bias conductance peak (ZBCP) in the realistic Majorana nanowire. The importance of this signature becomes further enhanced, particularly after the 2018 Nature paper, which displayed the quantized Majorana conductance, got retracted. In Chapter 2, the proposed quality factors quantify the robustness of quantized ZBCPs. By comparing the numerical results between different scenarios, this study shows that the quality factor $F$ can help distinguish topological MZMs from trivial subgap bound states in the low-temperature limit.

Another necessary signature of MZMs is the non-local correlation. In Chapter 3, the conductance correlation is demonstrated by modeling the comparing quantum-point-contact (QPC) conductance from each end. Both the pristine nanowire and the quantum-dot-hybrid-nanowire system are modeled and compared, which shows the significance of non-local end-to-end correlation for the existence of MZMs. The other approach to simultaneously examining the localization of states at both ends of the nanowire is through the Coulomb blockade (CB) measurement. The lack of sensitivity to the localized state at only one end makes the CB spectroscopy able to capture the non-local correlation feature of MZMs. However, CB transport in the Majorana nanowire is much more complicated to analyze than QPC transport because (a) Coulomb interaction is treated as equal to MZM physics without perturbation, and (b) there are many energy levels in the nanowire, which gives rise to an exponential complexity to solve the rate equations. In Chapter 4, a generalized version of Meir-Wingreen formula for the tunneling conductance of a two-terminal system is derived. This formula reduces the exponential complexity of the rate equations to as low as the linear complexity of QPC tunneling, thus allowing multiple energy levels to be included in the calculation. With dominant realistic effects in the model, the experimental features, such as the bright-dark-bright CB conductance pattern and decreasing oscillation conductance peak spacings (OCPSs) with the Zeeman field, will be simulated and explained theoretically.

In short, the theoretical methods proposed in this thesis, including the quality factors, non-local correlation ZBCPs, and CB spectroscopy, are intended to distinguish MZMs from other topologically trivial bound states. Further investigations on the robustness of quantized conductance and non-local correlation analysis can clarify the ambiguous signals in the experiments and push the realization of topological quantum computation to the frontier.

In this dissertation, we discuss the applications of intense mid-infrared laser interactions in three main topics. First, we demonstrate and discuss the remote detection of radioactive materials using avalanche breakdowns driven by picosecond, mid-infrared laser pulses. In the presence of radioactive materials, an enhanced population of free electrons and weakly bound ions are created in air. Laser driven avalanche ionization is a powerful tool for amplifying and detecting this weak signature, allowing for detection at standoff distances beyond the stopping distance of the radioactive particles. This technique can be applied more generally to the detection of any low density plasma. In the second section, we apply a similar method to measure laser ionization yields in atmospheric pressure gas across an extremely wide range. Finally, we demonstrate and discuss the generation of THz and low harmonics from two-color mid-infrared laser pulses. This technique allows for the generation of highly efficient, ultra-broadband coherent radiation.

Majorana zero modes are neutral zero-energy localized excitations emerging in the low-dimensional condensed matter systems, which are their own antiparticles. These excitations are topological with an intrinsic ground-state degeneracy, belonging to the (SU­₂­)₂ algebra and obeying the non-Abelian anyonic braiding statistics, which provides a possibility to implement the fault-tolerant topological quantum computing. As a result, enormous experimental efforts have focused on the realization of the Majorana zero modes, especially in the one-dimensional superconductor-semiconductor Majorana nanowires during the past decade. Although experiments have observed the zero-bias conductance peaks, these experimentally observed peaks are not robustly quantized as theoretically predicted for the signature of Majorana zero modes, and many other hallmarks of Majorana zero modes are yet to be unambiguously confirmed in experiments, which makes the experimentally observed zero-bias conductance peaks being interpreted as the Majorana zero modes questionable.

Therefore, in this dissertation, we carry out a detailed theoretical analysis of the experimental results, and classify the experimentally observed zero-bias conductance peaks into three types: the good (i.e., the actual topological Majorana zero modes), the bad (i.e., which is the partially-separated quasi-Majorana modes induced by the inhomogeneous potential and quantum dot in the nanowire), and the ugly (i.e., which is the trivial low energy fermionic state induced by random disorder). Our study concludes that almost all the current experimentally observed zero-bias conductance peaks in the publications are the ugly zero-bias conductance peaks, and future experiments should focus on the improvement of the material quality to reduce disorder.

Cold atoms trapped in optical lattices have been proven to be a versatile, well-controlled and powerful platform for simulating and studying physics, from condensed matter systems to high energy physics and cosmology. However, the diffraction limit restricts the spatial resolution of light-induced confinement and measurement. Since the length scale of confinement sets a characteristic energy scale of the system, it is desirable to circumvent this diffraction limit to provide more control of the associated energy scale.

In the first half of this thesis, I describe a series of experiments that exploit the nonlinear optical response in the three-level system of 171Yb to realize subwavelength spatial control and measurement of cold atoms. First, I report the experimental realization of a conservative optical lattice for cold atoms with subwavelength spatial structure. The three-level system is coupled by two laser fields in a way that the dark state of the three-level system changes its spin composition over a narrow spatial region. The kinetic energy associated with this large gradient in the spin composition creates a lattice of narrow barriers with a width of 10 nm, which is one-fiftieth of the laser wavelength. Extending from this, I describe the realization of a wave-function density microscope with a spatial resolution of 10 nm and temporal resolution of 500 microseconds. Using the sharp spatial dependence in the spin composition of the dark state, we shelve narrow slices of the wavefunction within every unit cell of the lattice into selected spin state, which is then selectively read out to achieve subwavelength measurement of the atomic probability density. Finally, I report the stroboscopic realization of a λ/4-spaced lattice. We stroboscopically apply shifted versions of the lattice of narrow barriers mentioned earlier, thereby creating an effective time-averaged potential with a lattice spacing of λ/4.

In the past decade, significant progress has been made by extending the control of atoms to the single atom level, and single neutral atoms optically trapped in arrays have emerged as a compelling and scalable platform for quantum simulation and computing. A natural step is to extend to multi-species systems, which will help solve challenges encountered in single-species platforms.

In the second half of the thesis, I motivate and describe the construction of a new dual-species tweezer array apparatus. An inherent challenge in single-species platforms is the crosstalk between atoms due to the scattered photons from nearby atoms during site-selective control and measurement. A dual-species architecture with Rb and Yb can suppress unwanted crosstalk and even allow parallel tasking on Rb and Yb separately due to the large separation in resonance frequencies. Moreover, the use of multi-species atoms provides an extra tuning knob that is useful in realizing multi-qubit gates. By manipulating the substantial difference in the intra- and inter-species van der Waals force, multi-qubit gates could be realized on Rb and Yb, giving significant speedups for some quantum algorithms and error-correction schemes.

This thesis deals with the rigorous analysis of two models of superfluidity. One of them is a macro-scale description of the interacting dynamics of a mixture of superfluid Helium and normal Helium. The equations used are modifications of the incompressible Navier-Stokes equations in 2D, with a nonlinear mutual friction that couples the two fluids. We show global well-posedness of strong solutions (with high-regularity data) to this model, by proving a Beale-Kato-Majda-type condition.

Next, we study a micro-scale model (the “Pitaevskii’’ model) of superfluid-normal fluid interactions, derived by Lev Pitaevskii in 1959. This involves the nonlinear Schrödinger equation and incompressible inhomogeneous Navier-Stokes equations. Mass and momentum exchange between the two fluids is mediated through a nonlinear and bidirectional coupling. We establish the existence of local solutions (strong in wavefunction and velocity, weak in density) that satisfy an energy equality.

Finally, we prove a weak-strong type uniqueness theorem for the solutions of the Pitaevskii model.  We begin by arguing that for weak solutions whose regularity is governed purely by the energy balance equation, it is not possible to prove weak-strong uniqueness, even if the strong solution is as smooth as one wishes. Thus, we are forced to consider slightly less weak solutions obtained from a higher-order energy bound. Owing to their better regularity, we can compare them to moderate solutions – which are rougher than conventional strong solutions used for this purpose – and establish a weak-moderate uniqueness theorem. Relative to the solutions actually constructed in the earlier part of this thesis, only some of the regularity properties are used, allowing room for improved existence theorems in the future, while maintaining compatible uniqueness results.

Quantum systems are prone to noises. Accordingly, many techniques are developed to cancel the action of a quantum operation, or to protect the quantum information against the noises. In this dissertation, I discuss two such schemes, namely the recovery channel and the quantum error correction, and various scenarios in which they are applied.

The first scenario is the perfect recovery in the Gaussian fermionic systems. When the relative entropy between two states remains unchanged under a channel, the perfect recovery can be achieved. It is realized by the Petz recovery map. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel.

The second scenario is the approximate recovery in the context of quantum field theory. When perfect recovery is not achievable, the existence of a universal approximate recovery channel is proven. The approximation is in the sense that the fidelity between the recovered state and the original state is lower bounded by the change of the relative entropy under the quantum channel. This result is a generalization of previous results that applied to type-I von Neumann algebras. To deal with quantum field theory, the type of the von Neumann algebras is not restrained here. This induces qualitatively new features and requires extra proving techniques. This results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms.

The third scenario is applying quantum error correction codes on tensor networks on hyperbolic planes. This kind of model is proposed to be toy models of the AdS/CFT duality, thus also dubbed holographic tensor networks. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility, we provide guidelines for constructing networks consisting of multiple types of tensors which are efficiently contractible variational ansatzes, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. An explicit construction of such networks is also provided. It approximates the holographic HaPPY pentagon code when variational parameters are taken to be small.

Topological quantum error-correcting codes are a family of stabilizer codes that are built using a lattice of qubits. The stabilizers of the code are local, and logical information is encoded in the non-local degrees of freedom. From the condensed matter perspective, their code space corresponds to the ground state subspace of a local Hamiltonian belonging to a non-trivial topological phase of matter. Conversely, one can use fixed point Hamiltonian of a topological phase to define a topological quantum error-correcting code.

This close connection has motivated numerous studies which utilize insights from one viewpoint to address questions in the other. This thesis further explores the possibilities in this direction. In the first two parts, we present novel schemes to implement logical gates, which are motivated by the condensed matter perspective. In the third part, we show how the quantum error correction perspective could be used to realize robust topological entanglement phases in monitored random quantum circuits. And lastly, we explore the possibility of extending this connection beyond topological quantum error-correcting codes. In particular, we introduce an order parameter for detecting k-local non-trivial states, which can be thought of as a generalization of topological states that includes codewords of any quantum error-correcting code.

Analyzing time series from complex dynamical systems in nature is a common yet challenging task in scientific computation since these time series are usually high-dimensional. To apply our physics intuitions to these dynamical systems often requires projecting these time series to certain low-dimensional degrees of freedom, which often introduces complicated memory effect. In this work, we examine such memory effect within time series generated from Langevin dynamics, Molecular Dynamics (MD) and Monte Carlo (MC) simulations, and some experimental time series. We also develop computational methods to minimize and model such memory effects using statistical mechanics and machine learning.

In recent years, MD simulation has become a powerful tool to model complex molecular dynamics in physics, chemistry, material science, biology, and many other fields. However, rare events such as droplet formation, nucleation, and protein conformational changes are hard to sample using MD simulations since they happen on the timescales far away from what all-atom MD simulation can reach. This makes MD simulation less useful for studying the mechanism of rare event kinetics. Therefore, it is a common practice to perform enhanced sampling techniques to help sample rare events, which requires performing dimensionality reduction from atomic coordinates to a low-dimensional representation that has a minimal memory effect.

In the first part of this study, we focus on reducing the memory effect by capturing slow degrees of freedom using a set of low-dimensional reaction coordinates (RCs). These RCs can then be used to help reproducing correct kinetic connectivity between metastable states using enhanced sampling methods such as metadynamics. We demonstrate the utility of our method by applying them to the droplet formation from the gaseous phase of Lennard-Jones particles and the conformational changes of a small peptide Ace-Ala$_3$-Nme.

The second part of the study aims at modeling another type of memory coming from intrinsic long-term dependency induced by ignored fast degrees of freedom wherein we utilize one of the fundamental machine learning techniques called the recurrent neural network to model non-Markovianity within time-series generated from MD simulations. This method has been shown to work not only on the molecular model of alanine dipeptide but also on experimental time series taken from single-molecule force spectroscopy. At the end of this second part, we also improve this method to extrapolate physics that the neural network had never seen in the training dataset by incorporating static or dynamical constraints on the path ensemble it generates.

In this thesis we describe a novel regime of cavity quantum electrodynamics, where a single atom is coupled to a multi-mode Fabry-Perot cavity with a strength much larger than its free spectral range. In this regime, the atom acting as a quantum impurity mediates interactions between many-body states of radiation in the multi-mode cavity. This novel regime of cavity QED is experimentally realized by coupling superconducting artificial atoms to a high impedance 1-D superconducting transmission line cavity. We study the problem of single photon decay in these strongly non-linear cavities with discrete energy levels. By engineering the properties of the artificial atoms, we alter interaction and connectivity between many-body states of radiation, and we observe two distinct effects. For the case of a multi-mode Fabry-Perot cavity coupled to a fluxonium artificial atom, the interactions mediated by the atom attempts to split a single photon into two low frequency photons but fails because of limited connectivity in the many-body Fock space. This phenomenon of many-body localization of radiation gives rise to striking spectral features where a single standing wave resonance of the cavity is replaced by a fine structure of satellite peaks. On the other hand, for the case of a transmon coupled galvanically to the cavity, the interaction splits a single photon at high energy into a shower of odd number of lower energy photons. In this case the single standing wave resonance of the cavity acquires a shorter lifetime which can be calculated using Fermi's golden rule and matches our theoretical model without any adjustable parameters.

This dissertation explores quantum computing applications of fluxonium superconducting circuits. Fluxonium's high coherence time T₂ and anharmonicity make it an excellent platform for both digital quantum processors and analog quantum simulators. Focusing on the digital quantum computing applications, we report recent work on improving the T₂ and gate error rates of fluxonium qubits. Through enhancements in fabrication methods and engineering of fluxonium's spectrum, a coherence time in excess of 1 millisecond is achieved, setting a new standard for the most coherent superconducting qubit. This highly coherent device is used to demonstrate a single-qubit gate fidelity greater than 99.99%, a level of control that had not been observed until now in a solid-state quantum system. Utilizing the high energy relaxation time T₁ of the qubit transition, a novel measurement of the circuit's parity-protected 0-2 transition relaxation time is performed to extract additional sources of energy loss.

To demonstrate fluxonium's utility as a building block for analog quantum simulators, we investigate how to simulate quantum dynamics in the Transverse-Field Ising Model (TFIM) by inductively coupling 10 fluxonium circuits together. When the fluxonium loops are biased at half integer values of the magnetic flux quantum, the spectrum is highly anharmonic, and the qubit transition is well-approximated by a spin-1/2. This results in an effective Hamiltonian that is equivalent to the TFIM. By tuning the inter-qubit coupling across multiple devices, we can explore different regimes of the TFIM, establishing fluxonium as a prominent candidate for use in near-term quantum many-body simulations. 

Cells can sense and adapt motility to various external cues, such as chemoattractant, dc electric fields (EFs), and the physical properties of surroundings. This ability is essential to maintain normal physiological processes, and the malfunction may lead to severe diseases, such as cancer and autoimmune disease. Recent studies have observed waves of colocalized actin, associated with its upstream signaling molecules, drive cell directional migration. Furthermore, a coupled signal transduction excitable system – cytoskeleton excitable system (STEN-CEN) was revealed to regulate wave formation in the non-neural cell types. The system display hallmarks of excitability, such as refractory periods, all-or-none type response, and wave behaviors. Changing the states of STEN-CEN leads to the transition of migrational modes, which are typically observed across cell types.

This dissertation uses molecular experiments, computer vision quantification techniques, and modeling to understand how cells sense different external cues. Numerous studies have shown that there exist multiple parallel signal pathways sensing certain external stimuli, which suggests that the external signal is not sensed by a single molecule. Here I investigate the possibility of the STEN-CEN wave as the sensing unit to external cues. To overcome the challenge that wave dynamics are coupled with cell motion in normal-sized cells, I electro-fuse tens of Dictyostelium discoideum (D. d) cells together to giant cells. In giant cells, waves are no longer localized at the cell perimeter. The larger basal membrane area provides the opportunity to study the subcellular dynamics. I record the dynamics of F-actin and phosphatidylinositol (3,4,5)-triphosphate (PIP3), which represent CEN and STEN, respectively. To further decouple STEN and CEN, I apply a variety of chemical perturbations to suppress/activate STEN and CEN separately. Because the wave properties characterize the stage of STEN-CEN, I develop a series of quantification tools to measure wave area, duration, and speed. I collaborate with theorists to create a reaction-diffusion system model that recreates the experimental results.

The dissertation focuses on studying the role of STEN-CEN waves in sensing nanotopography and dc EF. CEN is found to directly sense the nanotopographical cue, forming long-lasting F-actin puncta at ridges in the absence of STEN. At the same time, STEN is essential for long-range wave behaviors for macro-domain nanoridges sensing. STEN and CEN cooperate in the sensing of the EF signals. According to the quantitative studies of wave properties, nanotopography changes the dimensionality and lifetime of waves, while EF can alter the activation thresholds of the intracellular systems. In summary, this thesis shows that the excitable biomechanical and biochemical wave system act as the sensing unit to the physical properties of the extracellular environment. As a result, cells can dynamically sense their surroundings and coordinate intracellular processes to migrate under the external cue guidance.

In this thesis, we present a theoretical study of energy absorption in chaotic systems subject to a rapid, time-periodic external drive. Periodic driving can facilitate a rich range of classical and quantum dynamical behaviors, including synchronization, dynamical stabilization, and chaos. Recent theoretical and experimental work has aimed to identify nonequilibrium “phases of matter” that might emerge in periodically driven systems, including prethermal states and discrete time crystals. However, energy absorption poses a potential obstacle to stabilization of these nonequilibrium states, particularly in quantum systems, where the persistence of the system’s quantum properties may be contingent on careful isolation of the system from its environment. For these systems, energy gain from the drive cannot be balanced by dissipation into a thermal bath, and so the only way to maintain a steady state is to suppress energy absorption entirely. As a result, much work has been devoted to understanding energy absorption, and the conditions under which it might be suppressed, in periodically driven, thermally isolated classical and quantum systems.

Motivated by these general concerns, we narrow our focus towards model systems with chaotic, ergodic dynamics; such models are the cornerstone of the modern understanding of statistical mechanics and thermalization. Specifically, we begin our analysis with classical periodically driven chaotic systems, in the high-frequency driving regime. In this limit, we find that energy absorption in these systems is described by a process of diffusion in energy space. This energy diffusion model predicts a three-stage process of energy evolution: Initial relaxation to a prethermal state, followed by slow evolution of the system’s energy probability distribution in accordance with a Fokker-Planck equation, followed by either unbounded energy absorption or relaxation to an infinite temperature state. The rate of energy absorption predicted by this model is found to be consistent with a range of theoretical and numerical studies of both classical and quantum systems, which have found heating rates which are exponentially or quasi-exponentially small in the frequency of the drive.

After investigating the general features of the energy diffusion description, we then explore this framework as it applies to different classes of systems. First, we look at energy absorption in dynamical billiard models, in which a particle in a cavity is subjected to a rapid periodic driving force. For these systems, we obtain simple, explicit expressions for the rates of energy absorption and diffusion, and we find good agreement between these results and numerical simulations. Moreover, we find that this analysis for billiard models may be generalized to many-particle billiard systems, offering a window into how energy absorption can occur in many-body interacting systems. We then apply the energy diffusion description to one-dimensional oscillator systems, driven by weak noise. For these systems, the Fokker-Planck equation describing energy diffusion is especially simple and can be solved exactly in some cases. Finally, we look to periodically driven quantum chaotic systems, and begin to probe whether such systems may be described by the classical energy diffusion model. We discuss the theoretical tools necessary to understand this possible connection, including Floquet theory and random matrix theory. We conclude with a heuristic model of quantum energy absorption, which exhibits this quantum-classical correspondence in the semiclassical limit.

Quantum dot spin qubits are a promising platform for realizing quantum information technologies, which can theoretically perform calculations such as factoring large integers that are otherwise intractable using classical computing methods. However, quantum dot qubit technology is still in its developmental phases, with current experimental devices capable of holding only a few (less than 10) noisy qubits. However, even with only a small number of quantum dots, interesting experiments can be performed, simulating physical systems and observing many-body phenomena which are otherwise difficult to study or numerically simulate classically.

In this thesis, we analytically examine valley states in Silicon, which is one obstacle which can potentially lead to information loss in Silicon qubits. Using a perturbative method, we calculate the dynamics of two exchange-coupled quantum dots in which there is a valley degree of freedom. We find that the spin states can become entangled with the valley states of the system if the electrons are not initialized to the correct valley states, which can adversely affect quantum computations performed on these systems. We then detail how quantum dot plaquettes can simulate the Hubbard model and give many analytic results for different magnetic phenomena that arise under this model. These results include examples of Nagaoka ferromagnetism, violations of Hund's rule, and situations where flatband ferromagnetic ground states are necessarily degenerate with nonferromagnetic states. These phenomena all require only a few quantum dots and are observable with current experimental technologies.

Complex scatterings exist in many diverse physical and real-life scenarios. Examples include atomic nuclei, quantum dots, and electromagnetic (EM) waves in resonant systems. These systems are Chaotic, meaning that minute perturbations will lead to a drastic change in the properties of the system. The underlying chaotic property makes deterministic modeling of wave properties vulnerable to small perturbations. Because of this, statistical methods play a central role in chaotic system studies. The Random Coupling Model (RCM) has been successfully applied to predicting the statistics of single chaotic EM enclosures. We here expand RCM to systems consisting of multiple volumes, and do so with highly reduced computational complexity. Going beyond knowledge-based modeling, we employ machine-learning techniques to identify hidden information in chaotic systems.

Reservoir computing (RC) is a genre of neural network. Its training is radically simplified because the input and reservoir layers stay unchanged during the process. Recent work shows that RC can reasonably predict the future evolution of spatio-temporal chaotic systems. We aim to reverse the thinking: to emulate a software RC using the spatio-temporal chaotic wave fields in physical EM enclosures. A proof-of-principle hardware RC is demonstrated experimentally.

The concept of photonic topological insulator (PTI) is translated from the study of topological insulators (TIs) in condensed matter physics. For a TI material, the charge will only flow in topologically-protected states on the boundary surrounding the material, rather than in the bulk. And thus the conductivity of the TI is topological: a bulk insulator and an edge conductor at the same time. We experimentally demonstrated a PTI system with quantum Hall (QH) and quantum spin Hall (QSH) topological phases. The TI effect also introduces a synthetic spin-1/2 degree-of-freedom to light. The Fermionic two-state property, absent in the bosonic photon world, is now accessible using the PTI system. Using PTIs, we aim to realize a chaotic system, namely the Gaussian Symplectic Ensemble (GSE) statistical group, which in principle only exists in the Fermionic world. We use simulations to show that GSE statistics will emerge in an appropriately designed PTI graph containing anti-unitary symmetry.

Lattice QCD methods provide non-perturbative access to observables in QCD. However, there are still many aspects of QCD yet to be revealed on the lattice due to the numerical difficulties called sign problems. In this talk, I will discuss recent developments on methods to alleviate or solve the real-time sign problem, which appears in Minkowski lattice calculations. Approaches to the real-time sign problem are different on classical and quantum computers, and this talk mainly focuses on classical algorithms. One well-established way to alleviate sign problems is the so-called manifold deformation method, in which one deforms the manifold of integration in the path integral to the complex plane, aiming for a milder sign problem. I will show that this method is expected to solve the real-time sign problem in bosonic lattice field theories. I will describe an algorithm based on machine learning to deform the manifold of integration toward a manifold without the sign problem. 

Theoretical physics research often requires the most advanced mathematical techniques, ranging from geometry and calculus to numerical methods and data-driven techniques used on high-performance computers. As one of the most complex and demanding sub-domains of physics nowadays, quantum information science challenges scientists to leverage and expand our toolbox in order to analyze and comprehend quantum mechanical systems. This dissertation provides a quick overview of the various hardware platforms and describes an analytical toolbox implemented in quantum information science. This toolbox contains the three most used methodologies in modern scientific research: analytical modeling, numerical simulation, and machine learning. We address historical contexts, technical specifics, application examples, and the advantages and downsides of each approach. We focus on three case studies to show the usage of this integrated analytical toolbox: First, as a qubit noise reduction study, we describe a giant atom dissipation process using a superconducting qubit coupled nonlocally to a mechanical waveguide; Second, as a quantum control optimization problem, we design a feedback cooling strategy based on a toy model of weakly monitored Bose-Einstein condensates. At last, as an image data analysis, we employ neural network architectures to classify and analyze our experimental dataset automatically.

Interest in correlated electron states in strongly correlated materials, such as transition metal dichalcogenides (TMDs), has been growing in recent years thanks to significant technological advancements in cryogenic quantum optics measurement techniques that allow for their experimental realization. Milli-kelvin temperatures are required to eliminate thermalization effects that otherwise mask the interesting correlated physics in these materials. In an effort to contribute to the understanding of these states, we developed an ultra-low temperature dilution refrigerator measurement system with free-space optical access that is able to achieve a base temperature of  <30 milli-kelvin and apply a ±12 T perpendicular magnetic field. We utilize a 100x cryogenic objective with 0.82 NA to make highly localized optical measurements on our samples. Our custom stage system allows for quick sample exchange and rapid characterization of our devices.

TMDs have been shown to be suitable materials for probing new and interesting exciton physics. In monolayer form, their direct band gap in the visible range and high binding energies open the possibility to optically explore higher energy Rydberg states. As the understanding of the neutral exciton's Rydberg series has grown in recent years, interest has started to shift toward the less understood charged excitons.  Using photoluminescence excitation (PLE), we sweep a laser's energy  across the spectral range of the n>1 Rydberg exciton states and monitor the emission intensities of the 1s excitons. Through this technique, we were able to measure the precise spectral profile and carrier density dependence of the 3s neutral (X₀^3s), 2s neutral (X₀^2s ), and 2s negatively charged (X_-^2s) excitons in monolayer WSe₂. By applying a perpendicular magnetic field to the sample, we were also able to measure the valley dependent Zeeman splitting of both X₀^2s and X_-^2s and extracted their corresponding g-factors.

A Josephson junction (JJ) is known as a weak link connecting two superconductors, in which the non-dissipative supercurrent flows. More than two superconductors also can form a single composite JJ, called a “multi-terminal JJ”, by being connected through a common weak link. The supercurrent in multi-terminal JJs may depend on multiple superconducting phase differences defined across the junction, which is attributed to the supercurrent-carrying sub-gap quasiparticle bound states called Andreev bound states (ABSs).

In this dissertation, we first investigate the supercurrent of three- and four-terminal JJs fabricated on hybrid two-dimensional Al/InAs (superconductor/semiconductor) heterostructures. We define the critical current of an N-terminal junction as a (N − 1)-dimensional hypersurface of the bias currents, which can be reduced to a set of critical current contours (CCCs) in the two-dimensional planes. The geometry of the CCCs are modified non-trivially in response to magnetic field, electrical gating and phase biasing, which is attributed to the multi-phase-dependent ABSs. We also show that our experimental observations are consistent with quantum transport simulations based on a tight-binding model of the hybrid superconductor/semiconductor system. Second, we demonstrate the multi-phase-dependence of ABSs in three-terminal JJs by tunneling spectroscopy measurements. The ABS energy spectrum mimics electronic band structure in solid, which makes multi-terminal JJs provide a new platform to study band topology in higher dimensional parameter space. Moreover, spin-splitting of ABS energies induced by the multi-phase and gapless energy spectrum facilitated by the presence of a discrete vortex, a nonzero winding of the superconducting phases, are investigated.

Monolayer two-dimensional transition metal dichalcogenides (2D TMDs) represent a class of atomically thin semiconductors with unique optical properties. Similar to graphene, but with a three-layer (staggered) honeycomb lattice, TMDs host direct-gap transitions at their ±K valleys that exhibit circular-dichroism due to their finite Berry curvature. The reduced dimensionality of materials in this system, combined with large effective carrier masses, leads to enhanced Coulomb interaction and extremely tightly bound excitons (E_B ≈ 150-300 meV). Here, we seek to exploit the unusually tight binding of the excitons to probe two different types of higher energy exciton species in TMDs.

First, we experimentally probe the magneto-optical properties of 2s Rydberg exciton species in WSe₂. The magnetic response of excitons gives information on their spin and valley configurations, nuanced carrier interactions, and insight into the underlying band structure. Recently, there have been several reports of 2s/3s charged excitons in TMDs, but very little is still known about their response to external magnetic fields. Using photoluminescence excitation spectroscopy, we verify the 2s charged exciton and report for the first time its response to an applied magnetic field. We benchmark this response against the neutral exciton and find that both the 2s neutral and charged excitons exhibit similar behavior with $g$-factors of   and , respectively.

Second, via theoretical calculations, we investigate the exciton spectrum generated in 2D semiconductors under illumination by twisted light. Twisted light carries orbital angular momentum (OAM) which can act as an additional tunable degree of freedom in the system. We demonstrate that twisted light does not have the ability to modify the exciton spectrum and induce dipole-forbidden excitons, in contrast to atoms. This result stems from the fact that the additional OAM is transferred preferentially to the center-of-mass (COM) of the exciton, without modifying the relative coordinate which would allow dipole-forbidden higher energy excitons to form.

Cell motility plays an integral role in most biological processes. One principle of motility is the protrusions and retractions of cellular membranes called pseudopods. The physical force behind pseudopod formation is actin polymerization. As the physical driver, actin polymerization integrates the cells' upstream biochemical signaling cascades and turns the signals into action as the combined output and readout of the state of the cell. Actin polymerization not only occurs within pseudopods but propagates throughout a cell in waves that can be understood and modeled as excitable media.

This dissertation focuses on actin wave dynamics in the context of directed cell migration using both experimental and numerical techniques. Directed cell migration is essential in physiological processes including embryonic development, cancer metastasis, and wound healing. In this thesis, I analyze how immune-like cells are guided by external stimuli that are common in wound environments: electric fields, chemical gradients, and surface texture. A focus of this work is on the emergent excitable wave behavior of actin, and the pseudopods they generate, in simplified, in vitro environments.

Actin waves have been previously shown to respond to and be guided by the topography of an underlying substrate. Additionally, static quantifications of actin filaments after electric field stimulation become asymmetrically distributed within the cytoplasm. In neutrophils, the combination of cues leads to higher control of cell motility by guiding the internal actin waves. Using an optical flow algorithm, I quantify the actin waves on multiple length scales to ascertain the role of each guidance cue in affecting cell motion. I find that the waves preferentially polymerize and travel along the nanoridge length. Actin waves nucleate preferentially on the cathode side and reorient the cells axis of polarity (i.e., the position of the dominant pseudopod).

The second example of competing guidance cues involves studying the collective motion of cells in response to cell-cell signal relay in competition with surface topography. We use Dictyostelium discoideum cells as a model system for this work, as they migrate collectively due to signal relay. The signal relay of these cells is similar to many immune cell species. Using a combination of image analysis tools and a coarse-grained stochastic model, we find that guidance by nanoridges overrides the chemical signal relay and forces cells to migrate individually, suppressing streaming behavior. We model both the secretion and propagation of chemical signals using an excitable systems framework. This work highlights that bidirectional signals can be effective at suppressing cell-cell attraction and streaming motion.

The response of immune cells to external stimuli in the wound environment is not universal. Macrophages---one of the largest immune cells---are observed to migrate in the opposite direction of the wound upon wound-induced electric field generation. In the third example, I study actin dynamics of M0 (resting) macrophage cells to elucidate the method in which these cells interact with external electric fields. This cell system exhibits oscillatory actin waves at rest. With electric field stimulation, the oscillatory actin waves start to generate protrusions. Without oscillations, the protrusions begin with actin-depleted regions, indicating that contractile elements are involved. This section highlights the different methods in which actin waves integrate external cues into cell responses in different biological contexts.