<p>Scientific progress often relies on unexpected discoveries and unique observations. In</p> <p>fact, many of the most groundbreaking scientific advances throughout history have been the</p> <p>result of serendipitous events. For instance, the discovery of penicillin by Alexander Fleming</p> <p>was a result of him noticing a mold growing on a petri dish that was contaminating his</p> <p>bacterial culture. Similarly, the discovery of the cosmic microwave background radiation,</p> <p>which is considered one of the strongest pieces of evidence for the Big Bang theory, was</p> <p>the result of two scientists accidentally stumbling upon it while conducting a completely</p> <p>different experiment. These types of unexpected discoveries can lead to new avenues of</p> <p>research and open up entirely new fields of study. During my PhD, I experienced a similar</p> <p>phenomenon when I stumbled upon an anomaly in my experimental data that led me down a</p> <p>completely new path of investigation. This unexpected discovery not only provided me with</p> <p>new insights into the underlying mechanisms of my research, but also opened new avenues for</p> <p>future research directions. It was a reminder that sometimes the greatest scientific progress</p> <p>can come from the most unexpected places.</p> <p>My primary focus was initially directed towards topological superconductivity. However,</p> <p>this research direction was modified by unexpected findings while characterizing a SQUID.</p> <p>Specifically, a unique response by a Josephson junction was observed when exposed to an inplane</p> <p>magnetic field. Chapter 1 details our experimental results on the SQUID. We observed</p> <p>intriguing effects resulting from the in-plane magnetic field in the asymmetric evolution of</p> <p>the Fraunhofer pattern suggesting the existence of additional underlying physics in the heterostructure,</p> <p>which may have been previously overlooked. This serendipitous finding served</p> <p>as the impetus to explore simpler superconducting devices such as nanowires and rings.</p> <p>Remarkably, subsequent investigations into the critical current of a superconducting ring revealed</p> <p>a bi-modal histogram arising from the application of an in-plane magnetic field, which</p> <p>was an unforeseen outcome. This adds to our observations made in chapter 1. Chapter 2 details</p> <p>the unique properties of Al-InAs superconducting rings. Further experiments involving</p> <p>a superconducting nanowire resulted in the observation of non-reciprocal critical current under</p> <p>an in-plane magnetic field perpendicular to the current direction, subsequently referred to as the superconducting diode effect. Chapter 3 delves into the non-reciprocal properties</p> <p>of an Al-InAs superconducting nanowire. Our findings revealed the diamagnetic source of</p> <p>non-reciprocity generic to multi-layer superconductors. Finally, chapter 4 provides a detailed</p> <p>account of the fabrication processes for the superconducting devices, along with a discussion</p> <p>of the measurement techniques employed to unveil the underlying physics.</p>

<p dir="ltr">Antiferromagnetic spintronics promises next-generation information processing devices with ultra-fast speeds and ultra-low power consumption. Inspired by the recent demonstration of signatures of Tunnel Magnetoresistance (TMR) in non-colinear chiral antiferromagnets of the Mn₃X family, we study the thermal stability of such magnets in both low and high barrier limits. A stochastic Landau-Lifshitz-Gilbert (s-LLG) based numerical assessment of the dynamics reveals that strong exchange fields in Mn₃Sn could lead to thermally-driven rapid fluctuations of the order parameter, viz., octupole moment. However, distinct Random Telegraph Noise (RTN)-like signals distinguish the high barrier limit from the low barrier limit - suggesting different physical phenomena in the two regimes. To that end, the correlation time for thermal fluctuations has been explored analytically following an approach inspired by Langer's theory in the high barrier limit and dephasing mechanisms in the low barrier limit. It has been shown that the dynamics in chiral antiferromagnetic nanoparticles in both regimes are an order of magnitude faster than easy plane ferromagnetic particles. The thermal instability of chiral antiferromagnets could lead to picosecond-scale random number generation in probabilistic bits -- paving the path toward ultra-fast probabilistic computation. </p>

Non-Abelian excitations, including Majorana fermions, parafermions, and Fibonacci anyons, provide potential new settings for realizations of topological quantum computation operations. Topological quantum systems have the advantage of being protected against some types of entanglement with the surrounding environment, but their elusive nature has inspired many to pursue rare systems in which they may be physically realized. In this work we present a new platform for production of parafermions in the ν=1/3 fractional quantum hall effect regime in a two-dimensional hole gas in a Gallium Arsenide quantum well, where spin transitions in the rich Γ₈ Luttinger ground state can be manipulated by gate-controlled electric fields. When numerical and analytical calculations of many-particle interactions combine with a proximity-induced superconducting pairing potential in this system, the spin transition we observe gives rise to a superconducting gap with an onset of six-fold degenerate ground state which disappears at critical values of the gap parameter Δ_k, the energetic signature associated with parafermion production.<br>

<p>In this dissertation, we present work on developing superconducting circuits intended to advance the implementation of Asynchronous Ballistic Reversible Computation using Fluxon Logic. In the first Chapter we introduce the need for developing reversible computing, and discuss implementing asynchronous reversible computing using fluxons in superconducting circuits. In Chapter 2, we introduce basic superconductivity physics, including the Josephson effects, which is necessary to know for understanding the behavior of Josephson junction transmission lines. In Chapter 3, we introduce tools to physically understand the behavior of topologically protected solitons, 'fluxons', in Josephson junction transmission lines. Finally, in Chapter 4, we briefly discuss the history of fluxon-based computation devices and present current state of the art design of such reversible computation devices, including the fluxon Rotary gate that we have developed. Taken together, these represent advances in the direction of implementing asynchronous reversible computing in practice.</p>

<p dir="ltr">Improvement in state-of-the-art molecular beam epitaxy has led to the growth of ultra-high-quality GaAs/AlGaAs heterostructures. Two-dimensional electron systems in GaAs/AlGaAs heterostructures have provided a platform for investigating numerous phenomena in condensed matter physics.</p><p dir="ltr">In Chapter 2, we study low-frequency charge noise in shallow GaAs/AlGaAs heterostructures using quantum point contacts as charge sensors. We observe that devices with an Al$_2$O$_33$ dielectric between the metal gates and semiconductor exhibit significantly lower charge noise than devices with only Schottky gates and no dielectric. The improvement in device stability allows the application of shallow structures for spin qubit projects, making gate potential sharply defined.</p><p dir="ltr">In Chapter 3, we investigated the impact of edge-edge interaction on an electronic Fabry-P\'erot interferometer in the quantum Hall regime. Recently, experimental observations of periodicity $\phi_0/2$ in the integer</p><p dir="ltr">quantum Hall regime has been attributed to an exotic electron pairing mechanism. We present measurements of a Fabry-P\'erot interferometer operated in the integer quantum Hall regime at filling factor $1\leq \nu \leq 3$. Like previous experimental reports, under specific conditions we observe oscillations with flux periodicity $\phi_{0}/2$. However, our data and analysis indicate that period-halving is not driven by electron pairing, as has previously been claimed in the literature, but rather, is the result of electrostatic coupling between multiple independent edge modes.</p><p dir="ltr">In Chapter 4, we demonstrated our attempts in realizing stable {\it in-situ} gating for probing the possible non-Abelian state $\nu=5/2$. Utilizing a trench gate technique on a doped AlGaAs sample exhibits reasonable gating in a standard experiment time scale. Introducing AlAs screening wells further enhances the stability; it also significantly improves the coherence of interference at both integer and fractional states. In the future work section, we propose possible heterostructure modifications to improve contact performance, 2DEG quality, and the coherence of the interference.</p>

The decline of Moore's law has catalyzed a significant effort to identify beyond-CMOS devices and architectures for the coming decades. A multitude of classical and quantum systems have been proposed to address this challenge, and spintronics has emerged as a promising approach for these post-Moore systems. Many of these architectures are tailored specifically for applications in combinatorial optimization and machine learning. Here we propose the use of spintronics for such applications by exploring two distinct but related computing paradigms. First, the use of spin-currents to manipulate and control quantum information is investigated with demonstrated high-fidelity gate operation. This control is accomplished through repeated entanglement and measurement of a stationary qubit with a flying-spin through spin-torque like effects. Secondly, by transitioning from single-spin quantum bits to larger spin ensembles, we then explore the use of stochastic nanomagnets to realize a probabilistic system that is intrinsically governed by Boltzmann statistics. The nanomagnets explore the search space at rapid speeds and can be used in a wide-range of applications including optimization and quantum emulation by encoding the solution to a given problem as the ground state of the equivalent Boltzmann machine. These applications are demonstrated through hardware emulation using an all-digital autonomous probabilistic circuit.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.