Classical and quantum dissipative dynamics in Josephson junctions: an Arnold problem, bifurcation and capture into resonance

TL;DR

This paper investigates the classical and quantum phase dynamics in Josephson junctions, focusing on bifurcation, resonance capture, and the Arnold probability, with implications for quantum measurement techniques.

Contribution

It introduces a comprehensive analysis of bifurcation and resonance capture in Josephson junctions, including quantum effects and the Arnold probability, advancing understanding of dynamical switching in superconducting circuits.

Findings

Derived the Arnold probability for classical and quantum regimes.

Numerically analyzed dynamical switching under nonequilibrium conditions.

Highlighted the role of bifurcation in qubit state readout.

Abstract

We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a point-like particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to non-demolition measurements such as high-fidelity readout of qubit states. We address the question `what is the probability of capture into either basin of attraction' and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.