The simplest model for superconductor electrodynamics are the London equations, which treats the impact of electromagnetic fields on the current density as a localized phenomenon. However, the charge carriers of superconductivity are quantum mechanical objects, and their wavefunctions are delocalized within the superconductor, leading to non-local effects. The Pippard equation is the generalization of London electrodynamics which incorporates this intrinsic non-locality through the introduction of a new superconducting characteristic length, \xi_0, called the Pippard coherence length. When building nano-scale superconducting devices, the inclusion of the coherence length into electrodynamics calculations becomes paramount. In this thesis, we provide numerical calculations of various electrodynamic quantities of interest in the non-local regime, and discuss their implications for building superconducting devices. We place special emphasis on Superconducting QUantum Inteference Devices (SQUIDs), and their usage as flux quantum bits (qubits) in quantum computation. One of the main limitations of these flux qubits is the presence of intrinsic flux noise, which leads to decoherence of the qubits. Although the origin of this flux noise is not known, there is evidence that it is related to spin impurities within the superconducting material. We present calculations which show that the flux noise in the non-local regime is signi cantly different from the local case. We also demonstrate that non-local electrodynamics greatly affect the self-inductance of the qubit.
Semiconductor-based superconducting qubits offer a versatile platform for studying hybrid quantum devices in circuit quantum electrodynamics (QED) architecture. Most of these circuit QED experiments utilize coplanar waveguides, where the incorporation of dc gate lines is straightforward. Here, we present a technique for probing gate-tunable hybrid devices using a three-dimensional (3D) microwave cavity. A recess is machined inside the cavity wall for the placement of devices and gate lines. We validate this design using a hybrid device based on an InAs-Al nanowire Josephson junction. The coupling between the device and the cavity is facilitated by a long superconducting strip, the antenna. The Josephson junction and the antenna together form a gatemon qubit. We further demonstrate the gate-tunable cavity shift and two-tone qubit spectroscopy. This technique could be used to probe various quantum devices and materials in a 3D circuit QED architecture that requires dc gate voltages.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.