Overdamped quantum phase diffusion and charging effects in Josephson junctions

TL;DR

This paper extends the classical Ivanchenko Zil'berman theory to include quantum effects in overdamped Josephson junctions at low temperatures, capturing charging effects and providing analytical current-voltage characteristics.

Contribution

It introduces a quantum extension of the classical phase diffusion model for Josephson junctions, incorporating charging effects and broadening the understanding of quantum phenomena in these systems.

Findings

Derived explicit current-voltage characteristics in the quantum regime.

Unified classical and quantum descriptions including Coulomb blockade and Cooper pair transfer.

Analytical results reduce to known classical limits in appropriate conditions.

Abstract

Exploiting the recently derived quantum Smoluchowski equation the classical Ivanchenko Zil'berman theory for overdamped diffusive phase motion of low capacitance Josephson junctions is extended to the low temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb blockade physics, coherent Cooper pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.