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AIP conference proceedings

Escape from a metastable potential in dissipative quantum and classical systems

D. A. Browne, Vinay Ambegaokar, Kenneth S. Chow

Published Jan 1, 1989• 1 citation
Publisher

Abstract

The resistively shunted Josephson Junction with an applied DC bias current has become a paradigm for studying the tunneling of a quantum object out of a metastable well in the presence of a dissipative environment. We use a simple kinetic theory approach to discuss the results of several experiments in the classical and the quantum regime, as well as the crossover between them. We also describe the enhancement of the tunneling in an applied microwave field.

DOI
10.1063/1.38766

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Physical review. B, Condensed matter•Dec 1, 1988•9 citations
The resistively shunted Josephson Junction with an applied DC bias current has become a paradigm for studying the tunneling of a quantum object out of a metastable well in the presence of a dissipative environment. We use a simple kinetic theory approach to discuss the results of several experiments in the classical and the quantum regime, as well as the crossover between them. We also describe the enhancement of the tunneling in an applied microwave field.
We develop a kinetic theory for the real-time response of a quantum particle interacting with a macroscopic reservoir. We calculate in the low-damping limit the width and bath-induced frequency shift of the metastable tunneling levels of a resistively shunted Josephson junction and the enhancement of the tunneling rate upon the application of a weak microwave field. The results agree with experiment without adjustable parameters. At low temperatures the equation of motion for the phase of the junction can be written as that of a spin-(1/2) object in a time-dependent magnetic field.
A new phase diffusive regime in a current biased Josephson junction is theoretically explored which originates from embedding the junction in a circuit environment with anomalous dissipation. This is realized by placing parallel to the junction a resistor in series with a capacitor such that electromagnetic fluctuations effectively couple also to the charge of the junction. This leads to rich Josephson dynamics, in particular for the switching of the junction out of a zero voltage state. Modelled as the escape process of a fictitious phase-particle out of a metastable well, a detailed study reveals that anomalous dissipation has a strong impact at low temperatures when quantum tunneling dominates against thermal activation. As a manifestation, a regime is found, where for realistic circuit parameters the quantum escape process is substantially enhanced, followed by a short voltage pulse and re-trapping with high probability. This class of circuits may be leveraged for detecting microwave photons or dissipative quantum annealing processes. In addition, the analysis provides a general framework for engineering dissipative dynamics in nonlinear systems using anomalous environments.
This chapter considers one important physical example of that kind, quantum dissipative decay of a metastable state. It demonstrates how to evaluate the quantum decay rate of a metastable state for a quantum particle in the presence of dissipation. In the presence of phase fluctuations, however, such current states become unstable and decay simply because the “particle” can escape from the local potential minimum either by thermal activation or by quantum tunneling. The chapter also considers sufficiently low temperatures in which case the decay is due to quantum tunnelling. Classical process of thermally activated decay of supercurrent in Josephson junctions was first demonstrated in 1974, and the results turned out to be in a good agreement with theoretical predictions. Later experiments allowed to quantitatively verify a number of important theoretical predictions, for example, ones concerning the effect of temperature and damping on the quantum decay rate.
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting realistic circuit parameters, we address the question of its experimental observability and discuss suitable parameter spaces for the observation of the enhanced rate.
We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multivalued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.
For a dissipative quantum system in the low-damping regime, we show that the master-equation description of the reduced density matrix reduces, in the semiclassical limit, to the energy-diffusion version of the Fokker-Planck equation. This result can be generalized to include non-Ohmic damping and an external harmonic perturbation. Results of calculations based on the master equation show good agreement with experiments on the resistanceless-to-resistive transition in Josephson junctions in the classical regime and with results of purely classical calculations.