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Physical review. B, Condensed matter

Josephson junction coupled to an open transmission line: An application to the theory of macroscopic quantum tunneling

Sudip Chakravarty, Albert Schmid

Published Feb 1, 1986• 40 citations
Publisher

Abstract

In view of recent interest in the subject of macroscopic quantum tunneling in Josephson junctions and superconducting quantum interference devices, an extension of the method of calculation of the tunneling rate is made to a distributed circuit model. The current understanding is based on a lumped circuit model. It is hoped that the results derived would be useful in the context of the present experimental efforts.

DOI
10.1103/physrevb.33.2000

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Qubits

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Quantum mechanics and superconductivity are intimately connected on many levels. Quantum mechanics is needed to understand why a metal is a metal. The BCS condensate of Cooper pairs would not exist without quantum mechanics, nor could Cooper pairs tunnel through the barriers of Josephson junctions. The name SQUID is the abbreviation of superconducting quantum interference device. Yet another level of quantumness has been added in the last two decades. It turns out to be possible to design and fabricate superconducting objects that have macroscopic dimensions and properties, but behave as if they are single quantum particles. Amplitude and phase of the superconducting wavefunction act as conjugate quantum variables. Practical devices and circuits make use of Josephson junctions to reach the parameter values that are needed, but there is a clear distinction from the Josephson electronics circuits in the other chapters of this book. The latter may, in this context, well be referred to as being classical.

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In view of recent interest in the subject of macroscopic quantum tunneling in Josephson junctions and superconducting quantum interference devices, an extension of the method of calculation of the tunneling rate is made to a distributed circuit model. The current understanding is based on a lumped circuit model. It is hoped that the results derived would be useful in the context of the present experimental efforts.
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Recent demonstrations of macroscopic quantum coherence in Josephson junction based electronic circuits have opened an entirely new dimension for research and applications in the established field of Josephson electronics. In this article we discuss basic Josephson circuits for qubit applications, methods of quantum description of these circuits, and circuit solutions for qubit couplings. Principles of manipulation and readout of superconducting qubits are reviewed and illustrated with recent experiments using various qubit types.
Macroscopic quantum effects in Josephson systems have attracted great interest in the scientific community both for the physics involved and in view of applications. We present data on macroscopic quantum tunneling on Josephson junctions. Actually the most fascinating topic is the observation of macroscopic quantum coherence in rf-SQUID. This effect also has implications for quantum computing, because a quantum two-state system represents a single quantum bit, which is the elementary unit of a quantum computer. In this context, here we present a new method to measure quantum coherence between different fluxoid states of an rf-SQUID by using the procedure of "adiabatic inversion". This method offers the possibility of measuring tunneling and decoherence times in the system.
This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. \nFor the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and \nuncertainties of circuit observables. \nMacroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits.
Quantum mechanics and superconductivity are intimately connected on many levels. Quantum mechanics is needed to understand why a metal is a metal. The BCS condensate of Cooper pairs would not exist without quantum mechanics, nor could Cooper pairs tunnel through the barriers of Josephson junctions. The name SQUID is the abbreviation of superconducting quantum interference device. Yet another level of quantumness has been added in the last two decades. It turns out to be possible to design and fabricate superconducting objects that have macroscopic dimensions and properties, but behave as if they are single quantum particles. Amplitude and phase of the superconducting wavefunction act as conjugate quantum variables. Practical devices and circuits make use of Josephson junctions to reach the parameter values that are needed, but there is a clear distinction from the Josephson electronics circuits in the other chapters of this book. The latter may, in this context, well be referred to as being classical.