Josephson effect with superfluid fermions in the two-dimensional BCS-BEC crossover

TL;DR

This paper studies the Josephson effect in two-dimensional fermionic superfluids across the BCS-BEC crossover, highlighting the limitations of mean-field models and analyzing tunneling dynamics and frequencies.

Contribution

It introduces an effective tunneling energy dependent on condensate fraction and chemical potential, improving understanding of Josephson dynamics beyond mean-field approximations.

Findings

Mean-field tunneling energy is unreliable in the BEC regime.

Josephson frequency peaks in the intermediate crossover regime.

Nonlinear tunneling oscillations are characterized across the crossover.

Abstract

We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase calculating the frequency of tunneling oscillation both in the linear regime and in the nonlinear one. Our results show that the Josephson frequency is larger in the intermediate regime of the BCS-BEC crossover due to the peculiar behavior of the effective tunneling energy in the crossover.