Quantum dynamics of two capacitively coupled superconducting islands via Josephson junctions

TL;DR

This paper models the quantum dynamics of two capacitively coupled superconducting islands with Josephson junctions, revealing their evolution into rotated-squeezed-coherent states and periodic Cooper pair number oscillations.

Contribution

It provides an exact solution for the quantum dynamics of coupled superconducting islands, reducing the system to harmonic oscillators and analyzing their evolution.

Findings

Cooper pair numbers oscillate periodically between the islands.

System evolves into rotated-squeezed-coherent states from initial coherent states.

Exact analytical solutions are obtained for the coupled system.

Abstract

In this paper, we consider a system consisting of two capacitively coupled superconducting islands via Josephson junctions. We show that it can be reduced to two coupling harmonic oscillators under certain conditions, and solved exactly in terms of a displacing transformation, a beam-splitter-like transformation, and a squeezing transformation. It is found that the system evolves by a rotated-squeezed-coherent state when the system is initially in a coherent state. Quantum dynamics of the Cooper pairs in the two superconducting islands is investigated. It is shown that the number of the Cooper pairs in the two islands evolves periodically.