Theory Of Electron Transport In Superconducting Heterostructures

Author : Corey I Ostrove
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (125 download)

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Download or read book Entanglement in Superconducting Heterostructures, and Quantum Circuit Simulation Hardware written by Corey I Ostrove and published by . This book was released on 2021 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: We begin this dissertation by studying noise correlations in superconducting heterostructures of various geometries. In recent years there has been a resurgence of interest in the nonlocal transport properties of superconducting heterostructures due to the possibility of their serving as a source of electronic entanglement in solid state quantum information processors. Devices designed for this purpose are called Cooper pair splitting devices. The utility of these devices as entanglement sources is known to have connections to the positivity of noise cross correlations in spatially separated leads. In Chapter 1 we outline the theoretical prerequisites for this work, outlining the scattering theory framework based on the Bogoliubov-de Gennes equations we adopt. Within this framework we apply a methodology first introduced by Demers and by Blonder, Tinkham and Klapwijk (BTK) in the early 1980s to find the scattering matrix for our superconducting structures. The current, local and nonlocal shot noise can all be expressed in terms of the underlying scattering processes. This framework allows us to investigate the behavior of the current and noise correlations in the structure as we change the geometry and other key system parameters such as the system size, superconducting phase difference and temperature. We also introduce the Andreev approximation, a commonly used approximation which simplifies the scattering theory for superconducting heterostructures. In Chapter 2, we study the local and nonlocal shot noise in a quasi-1D normal-superconducting-normal (NSN) geometry using material parameters relevant to high-T [subscript c] superconductivity. The scattering and shot noise distributions are studied in the short, intermediate and long system size limits, allowing us to examine the qualitative differences in these three parameter regimes. This allows us to, for example, identify the signatures of over-the-gap geometric resonances in the shot noise distributions that appear in the long system size limit. We also break the nonlocal shot noise distributions down further and study the individual contributions to the nonlocal shot due to particle-particle, hole-hole and particle-hole scattering processes. In Chapter 3, we extend our investigation of superconducting heterostructures to the more complicated NSNSN geometry. A novel feature introduced in the geometry is the presence of subgap quasibound states, which show up as resonances in the scattering matrix. We show that these quasibound states dramatically impact the nonlocal shot noise distributions in the system. At energies near the quasibound states the dominant transmission channel through the system is a process called particle-hole transmission, which results in sharp positive peaks in the nonlocal shot noise distribution of the system. The behavior of the nonlocal noise correlations as we change the size of the superconducting and normal regions is investigated and it is found that there is a "sweet spot'' with respect to the size of the superconducting regions that maximizes the positivity of the nonlocal noise distributions as well as a periodic-like behavior in the positivity of the noise distributions with respect to the normal region size. The results of the full scattering theory for the NSNSN geometry are compared to the results obtained using the Andreev approximation, where we find that the Andreev approximation breaks down at energies close to the quasibound state energies. In the second half of this dissertation we focus on work related to the development of a prototype special-purpose quantum circuit simulation device based on commercial off-the-shelf high-speed analog signal processing hardware. In Chapter 4 we introduce the embedding scheme used to represent quantum states and quantum gates in the frequency domain of a classical analog voltage signal. Experimental results are presented from an early two-qubit prototype device for the fidelity of the state generation and gate application circuits. In Chapter 5, a more in-depth investigation into the modeling of classical errors within our signal processing based simulation method is performed in terms of the effects this noise has on the results of the quantum computation being simulatied. It is shown, for example, that additive white gaussian noise (AWGN) in our system has the same effect as applying a depolarizing channel to the qubits in the simulation. We then perform a simulation of a simple quantum error correction (QEC) protocol using the device and show that, even in the presence of classical noise in the simulation hardware, an overall enhancement in the performance of gate operations as a result of applying QEC is observed