Quantum system dynamics with a weakly nonlinear Josephson junction bath

TL;DR

This paper studies how a weakly nonlinear Josephson junction chain affects the dynamics of a quantum LC oscillator, deriving a Markovian master equation and exploring duality and non-Markovian effects at finite temperature.

Contribution

It provides a perturbative calculation of the Josephson bath correlation function and establishes a duality relation between different energy regimes, with implications for engineered and disordered chains.

Findings

Markovian dynamics for the LC oscillator under certain conditions

Duality relation between large charging and Josephson energies

Non-Markovian effects at higher temperatures

Abstract

We investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we perturbatively calculate the correlation function of the Josephson bath to the leading order in the Josephson energy divided by the charging energy while keeping the cosine potential exactly. When the variation of the charging energy along the chain ensures fast decay of the bath correlation function, the dynamics of the LC oscillator that is weakly and capacitively coupled to the Josephson bath can be solved through the Markovian master equation. We establish a duality relation for the Josephson bath between the regimes of large charging and Josephson energies respectively. The results can be applied to cases where the charging energy either is nonuniformly engineered or disordered in the chain. Furthermore, we find that the Josephson bath may become non-Markovian when the temperature is increased beyond the zero-temperature limit in that the bath correlation function gets shifted by a constant and does not decay with time.