Effective description of tunneling in a time-dependent potential with applications to voltage switching in Josephson junctions

TL;DR

This paper introduces a method using a time-dependent imaginary potential to model quantum tunneling in dynamic barriers, specifically applied to voltage switching in Josephson junctions, enhancing understanding of their quantum behavior.

Contribution

The paper presents a novel approach to describe tunneling in time-dependent potentials using a time-dependent imaginary potential, applied to Josephson junction phase dynamics.

Findings

Reproduces features of voltage switching in Josephson junctions

Provides detailed insight into electric field coupling in tunneling

Validates approach with Gamow solutions for stationary problems

Abstract

We propose to use a time-dependent imaginary potential to describe quantum mechanical tunneling through time-varying potential barriers. We use Gamow solutions for stationary tunneling problems to justify our choice of potential, and we apply our method to describe tunneling of a mesoscopic quantum variable: the phase change across a Josephson junction. The Josephson junction phase variable behaves as the position coordinate of a particle moving in a tilted washboard potential, and our general solution to the motion in such a potential with a time-dependent tilt reproduces a number of features associated with voltage switching in Josephson junctions. Apart from applications as artificial atoms in quantum information studies, the Josephson junction may serve as an electric field sensitive detector, and our studies provide a detailed understanding of how the voltage switching dynamics couples to the electric field amplitude.