Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models

TL;DR

This paper investigates the emergence of a relative phase and Josephson dynamics between two weakly coupled Richardson models, revealing how phase coherence develops in small fermionic systems and how the critical current varies across the BCS-BEC crossover.

Contribution

It introduces a study of phase formation and Josephson effects in coupled Richardson models, highlighting the emergence of a relative phase even in small systems and analyzing current-phase relations.

Findings

A definite relative phase emerges even for ~10 pairs.

Critical current peaks at the BCS-BEC crossover.

Two-state model effectively describes the dynamics.

Abstract

We consider two weakly coupled Richardson models to study the formation of a relative phase and the Josephson dynamics between two mesoscopic attractively interacting fermionic systems: our results apply to superconducting properties of coupled ultrasmall metallic grains and to Cooper-pairing superfluidity in neutral systems with a finite number of fermions. We discuss how a definite relative phase between the two systems emerges and how it can be conveniently extracted from the many-body wavefunction: we find that a definite relative phase difference emerges even for very small numbers of pairs ~10. The Josephson dynamics and the current-phase characteristics are then investigated, showing that the critical current has a maximum at the BCS-BEC crossover. For the considered initial conditions a two-state model gives a good description of the dynamics and of the current-phase characteristics.