Self-consistent dynamics of a Josephson junction in presence of an arbitrary environment

TL;DR

This paper develops a microscopic theory for the dynamics of a Josephson junction interacting with an arbitrary electromagnetic environment, extending P(E) theory to superconducting systems and providing a self-consistent solution for small phase fluctuations.

Contribution

It extends P(E) theory to superconducting Josephson junctions, deriving a self-consistent dynamic description including Cooper pair and quasiparticle tunneling.

Findings

Derived a set of coupled correlation functions for the system

Provided an exact linear admittance Y(ω) for small phase fluctuations

Achieved a self-consistent solution for the junction dynamics

Abstract

We derive microscopically the dynamics associated with the d.c. Josephson effect in a superconducting tunnel junction interacting with an arbitrary electromagnetic environment. To do so, we extend to superconducting junctions the so-called P(E) theory (see e.g. Ingold and Nazarov, arXiv:cond-mat/0508728) that accurately describes the interaction of a nonsuperconducting tunnel junction with its environment. We show the dynamics of this system is described by a small set of coupled correlation functions that take into account both Cooper pair and quasiparticle tunneling. When the phase fluctuations are small the problem is fully solved self-consistently, using and providing the exact linear admittance Y({\omega}) of the interacting junction.