<p>Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold.</p> <p>We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques. </p> <p><br></p> <p>With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples.</p> <p>In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local</p> <p>threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model.</p> <p>Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and</p> <p>Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.</p>

Probing nonequilibrium dynamics in a trapped, inhomogeneous atomic quantum gas can be a challenging task because coexisting mass transport and spreading of quantum correlations often make the problem intractable. By removing density inhomogeneity in an atomic quantum gas and employing local control of chemical potential as well as interaction parameters, it is possible to perform quasi-particle control, initiate and probe collective quantum dynamics without or with a controlled mass flow. We report our experimental results toward quasi-particle control and nonequilibrium dynamics in a homogeneous two-dimensional quantum gas.

<div> Challenges in the semiconductor industry have resulted in the discovery of a plethora of promising materials and devices such as the III-Vs (InGaAs, GaSb, GaN/InGaN) and 2D materials (Transition-metal dichalcogenides [TMDs]) with wide-ranging applications from logic devices, optoelectronics to biomedical devices. Performance of these devices suffer significantly from scattering processes such as polar-optical phonons (POP), charged impurities and remote phonon scattering. These scattering mechanisms are long-ranged, and a quantitative description of such devices require non-local scattering calculations that are computationally expensive. Though there have been extensive studies on coherent transport in these materials, simulations are scarce with scattering and virtually non-existent with non-local scattering. </div><div> </div><div>In this work, these scattering mechanisms with full non-locality are treated rigorously within the Non-Equilibrium Green's function (NEGF) formalism. Impact of non-locality on charge transport is assessed for GaSb/InAs nanowire TFETs highlighting the underestimation of scattering with local approximations. Phonon, impurity scattering, and structural disorders lead to exponentially decaying density of states known as Urbach tails/band tails. Impact of such scattering mechanisms on the band tail is studied in detail for several bulk and confined III-V devices (GaAs, InAs, GaSb and GaN) showing good agreement with existing experimental data. A systematic study of the dependence of Urbach tails with dielectric environment (oxides, charged impurities) is performed for single and multilayered 2D TMDs (MoS2, WS2 and WSe2) providing guideline values for researchers. </div><div><br></div><div>Often, empirical local approximations (ELA) are used in the literature to capture these non-local scattering processes. A comparison against ELA highlight the need for non-local scattering. A physics-based local approximation model is developed that captures the essential physics and is computationally feasible.</div>

Rare-earth ions in crystalline hosts have been identified as attractive media for quantum optical applications where record-high coherence times, quantum storage efficiency in solids, and quantum storage bandwidth have been demonstrated. Among rare-earth ions, Erbium uniquely possesses optical transitions at 1.5 micrometer region, making it suitable for integration with fiber telecommunication and silicon photonics. However, the intra-4f optical transitions are parity forbidden for rare-earth ions. Although, transitions are observed due to the interaction of the 4f valence electrons' energy levels with crystal fields or the lattice vibrations, the photon emission rate is prolonged for these ions. For example, Er³⁺ excited state lifetime for 1530nm transition is around 10 ms, which is about a million times longer than the excited state lifetime of alkali atoms like cesium and rubidium. There have been some recent works showing enhanced emission rate of erbium ions by about 10³ times by building a nano-photonic cavity to reach high Purcell factors. Our alternative approach to solving this problem is to use an ensemble of ions instead of a single ion to induce collective interactions in a suitable platform. In one experiment, we fabricated a SiN micro-ring resonator and implanted 10⁴ isotopically pure ¹⁶⁸Er ions in narrow segments located precisely in solids. The segments are typically separated by 0.962nm corresponding to multiples of the wavelength of Er emission at 1520nm. And we showed that when the lattice of ions is commensurate with the wavelength of the light, the scattering loss caused by the other ions is reduced. We have demonstrated for the first time that how designing atomic geometries in a solid-state photonic system can reduce the radiative loss due to spontaneous emission of ions into other photonic channels. This phenomenon is analogous to the Borrmann effect seen in x-ray transmissions of crystals at the Bragg angle of incidence. We have also shown how the interference between the optical cavity mode and atomic Bragg mode generates Fano-type resonance features. We performed these measurements using erbium ions in the SiN host. The limitations such as low coherence time and large inhomogeneous broadening in this platform prohibit observing cooperative and quantum behavior. To improve the optical property of erbium ions and study other cooperative effects, we engineered an effective ion array in an Er-doped Yttrium Orthosilicate crystal which can exhibit higher coherence time and narrower inhomogeneous broadening compared to SiN. So, we used the spectral hole burning technique to make an atomic grating in randomly distributed Er ions inside YSO. Two counter-propagating pump pulses created a standing wave inside the crystal, which enabled the creation of spectral holes only near the antinode locations. At the same time, atoms near nodes remain in the ground state. Such atomic population grating behaved like an atomic array. We have seen coherent backscattering up to 20% of the incident probe from this atomic grating resembling a mirror. To increase the reflection efficiency, we tried to increase the ion concentration in the YSO crystal. But, at high concentrations, the dipole-dipole interaction increases the broadening and decoherence rates of the ions. To increase the optical density without increasing the ion concentration, we fabricated long waveguides in SiN and LiNbO₃ with rare-earth ions implanted inside.As a future direction, we are trying to increase the reflection efficiency from the atomic grating to the point where we can see atomic mirror-assisted light trapping. We are also trying to see long-range co-operative behavior from rare-earth ion-doped crystals and rare-earth ions implanted inside long waveguides. This can open possibilities of new quantum photonic device engineering for applications in scalable and multiplexed quantum networks.

<p>As successful as the Standard Model has been in describing particle interactions, there are still many open questions it does not answer; the strong CP violation and the existence of dark matter among them. To address these issues many extensions to the Standard Model have been devised. Some of these extensions propose a new force mediating particle; a massive particle results in a potential described by a Yukawa-like interaction, while a massless exchange particle leads to power law type potentials. Limits on the strength of these interactions at the sub-micron range of separation between two particles are poorly characterized, but previous experiments conducted at IUPUI placed the best limits to date on the strength of a Yukawa-like interaction. Those experiments used a spherical test mass and a planar source mass. However, if a cylindrical test mass was used, the increased interaction volume of the cylinder would result in an increased sensitivity of about an order of magnitude over the spherical test mass experiment. Building such a system presents many challenges, namely the alignment of the cylinder with respect to the planar source mass. A capacitance based scheme to determine the alignment of a cylinder with respect to a plane will be discussed. The thesis concludes with an outline for a new type of measurement system. The new experiment attempts to induce a gravitational Π-pulse in a nanoshphere to probe extensions to the Standard Model.</p> <p> </p>

<div>The work involves two new method implementation and application in the Quantum transport community for nano-scale electronic devices. </div><div><br></div><div>First method: Ab-initio Tight-Binding(TB)</div><div> </div><div>As the surfacing of novel 2D materials, layers can be stacked freely on top of each other bound by Van der Waals force with atomic precision. New devices created with unique characteristics will need the theoretical guidance. The empirical tight-binding method is known to have difficulty accurately representing Hamiltonian of the 2D materials. Maximally localized Wannier function(MLWF) constructed directly from ab-initio calculation is an efficient and accurate method for basis construction. Together with NEGF, device calculation can be conducted. The implementation of MLWF in NEMO5 and the application on 2D MOS structure to demystify interlayer coupling are addressed. </div><div> </div><div>Second method: Büttiker-probe Recombination/Generation(RG) method:</div><div><br></div><div>The non-equilibrium Green function (NEGF) method is capable of nanodevice performance predictions including coherent and incoherent effects. To treat incoherent scattering, carrier generation and recombination is computationally very expensive. In this work, the numerically efficient Büttiker-probe model is expanded to cover recombination and generation effects in addition to various incoherent scattering processes. The capability of the new method to predict nanodevices is exemplified with quantum well III-N light-emitting diodes and photo-detector. Comparison is made with the state of art drift-diffusion method. Agreements are found to justify the method and disagreements are identified attributing to quantum effects. </div><div><br></div><div>The two menthod are individually developed and utilized together to study BP/MoS2 interface. In this vertical 2D device, anti-ambipolar(AAP) IV curve has been identified experimentally with different explanation in the current literature. An atomistic simulation is performed with basis generated from density functional theory. Recombination process is included and is able to explain the experiment findings and to provide insights into 2D interface devices.</div><div><br></div><div> </div>

<p>Holographic duality as a rigorous approach to quantum gravity claims that a quantum gravitational system is exactly equal to a quantum theory without gravity in lower spacetime dimensions living on the boundary of the quantum gravitational system. The duality maps key questions about the emergence of spacetime to questions on the non-gravitational boundary system that are accessible to us theoretically and experimentally. Recently, various aspects of quantum information theory on the boundary theory have been found to be dual to the geometric aspects of the bulk theory. In this thesis, we study the exact and approximate quantum error corrections (QEC) in a general quantum system (von Neumann algebras) focused on QFT and gravity. Moreover, we study entanglement theory in the presence of conserved charges in QFT and the multiparameter multistate generalization of quantum relative entropy.</p>

<p>One of the fundamental predictions of quantum mechanics is the occurrence of random fluctuations which can induce a measurable force between neutral objects, known as the Casimir effect. Casimir effect has attracted a lot of interest in both theoretical and practical work since the first prediction in 1948 because it is the most accessible evidence of quantum electromagnetic fluctuations in vacuum. Besides, it has prospective applications for nanotechnology and for studying fundamental physical theories beyond the standard model. In this dissertation, we report the experimental and theoretical progress towards realizing Casimir-based devices and long sought-after vacuum friction. </p> <p><br></p> <p>First, we propose and experimentally realize the first Casimir diode system that can regulate energy transfer along one direction through quantum vacuum fluctuations. This is the first experimental demonstration of non-reciprocal energy transfer by Casimir effects. We develop a dual-cantilever vacuum system which can be used to measure the Casimir force at separations from 50 nm to 1000 nm.  Parametric coupling scheme is applied to the system to couple two cantilevers with different resonant frequencies by Casimir interaction. By controlling the system near the exceptional point, we are able to break the time reversal symmetry and observe the non-reciprocal energy transfer. </p> <p><br></p> <p>The description of the Casimir diode system is followed by an experimental demonstration of the Casimir transistor system where we achieve the first measurement of Casimir interaction between three macroscopic objects. Three cantilevers can be coupled through quantum vacuum fluctuations by the parametric coupling scheme. Moreover, we have realized the first three-terminal Casimir transistor system that can switch and amplify quantum vacuum mediated energy transfer. These two Casimir-based devices will have potential applications in sensing and information processing.  </p> <p><br></p> <p>Subsequently, the first observation of Casimir mediated non-contact friction is demonstrated experimentally. When two parallel surfaces are moving with a relative velocity, they will experience quantum vacuum friction force which tries to slow down the relative motion because of quantum vacuum fluctuations. The quantum vacuum friction comes from the exchange of virtual photons between two moving bodies.  We have designed a novel method to detect the Casimir force mediated non-contact friction force between two harmonic oscillators. The non-contact friction comes from the interaction of virtual photons and phonons. We have experimentally detected the effect of non-contact friction and successfully measured the friction force at different velocities. </p> <p><br></p> <p>In the latter part of this thesis, two theoretical proposals about detecting the Casimir torque and rotational quantum vacuum friction torque by a levitated optomechanical system are discussed. The optically levitated nanoparticle system is a good candidate for precision measurements because it can achieve an ultrahigh mechanical quality factor due to the well isolation from the thermal environment. The calculation of the Casimir torque on a levitated nanorod near a birefringent plate is demonstrated. The calculation of the rotational quantum vacuum friction torque on a rotating nanosphere near a plate is also presented. By comparing these small torques to the sensitivity of our levitation system, we show that it is feasible to detect the Casimir torque and the rotational quantum vacuum friction torque under realistic conditions in the near future. </p> <p><br></p>