Phase diffusion and charging effects in Josephson junctions

TL;DR

This paper analyzes how phase diffusion and Coulomb blockade effects influence the supercurrent in Josephson junctions, providing a comprehensive theoretical framework for understanding current-voltage characteristics across different regimes.

Contribution

It presents a unified calculation of the Cooper pair current considering phase diffusion and Coulomb blockade effects using time-dependent perturbation theory.

Findings

Current-voltage characteristics derived in closed form.

Phase diffusion impacts the supercurrent in the classical regime.

Coulomb blockade causes a supercurrent peak in strong blockade regime.

Abstract

The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the strong Coulomb blockade regime.