Josephson current flowing through a nontrivial geometry: The role of pairing fluctuations across the BCS-BEC crossover

TL;DR

This paper models the Josephson effect in ultra-cold Fermi gases with complex geometries, incorporating pairing fluctuations across the BCS-BEC crossover at finite temperature, and successfully matches experimental data.

Contribution

It extends a theoretical approach to include pairing fluctuations in inhomogeneous environments, providing a detailed description of the Josephson effect in ultra-cold gases.

Findings

The model accurately reproduces experimental Josephson critical currents.

Pairing fluctuations significantly influence the Josephson effect in nontrivial geometries.

The approach reveals universal features of the Josephson effect in ultra-cold gases.

Abstract

A realistic description of the Josephson effect at finite temperature with ultra-cold Fermi gases embedded in nontrivial geometrical constraints (typically, a trap plus a barrier) requires appropriate consideration of pairing fluctuations that arise in inhomogeneous environments. Here, we apply the theoretical approach developed in the companion article [Pisani \emph{et al.}, Phys. Rev. B {\bf 108}, 214503 (2023)], where the inclusion of pairing fluctuations beyond mean field across the BCS-BEC crossover at finite temperature is combined with a detailed description of the gap parameter in a nontrivial geometry. In this way, we are able to account for the experimental results on the Josephson critical current, reported both at low temperature for various couplings across the BCS-BEC crossover and as a function of temperature at unitarity. Besides validating the theoretical approach of the companion article, our numerical results reveal generic features of the Josephson effect which may not readily emerge from an analysis of corresponding experiments with condensed-matter samples owing to the unique intrinsic flexibility of experiments with ultra-cold gases.