# Critical Josephson current in BCS-BEC crossover superfluids

## TL;DR

This paper presents a microscopic model for Josephson currents in ultracold fermionic superfluids across the BCS-BEC crossover, revealing a maximum near unitarity and matching experimental and numerical results.

## Contribution

It introduces an analytic model for the critical Josephson current that accounts for interaction strength and barrier height, extending previous bosonic models to fermionic superfluids.

## Key findings

- Critical current peaks near unitarity.
- Model agrees with experimental data.
- Analytic expressions valid for various coupling regimes.

## Abstract

We develop a microscopic model to describe the Josephson dynamics between two superfluid reservoirs of ultracold fermionic atoms which accounts for the dependence of the critical current on both the barrier height and the interaction strength along the crossover from BCS to BEC. Building on a previous study [F. Meier & W. Zwerger, Phys. Rev. A, 64 033610 (2001)] of weakly-interacting bosons, we derive analytic results for the Josephson critical current at zero temperature for homogeneous and trapped systems at arbitrary coupling. The critical current exhibits a maximum near the unitarity limit which arises from the competition between the increasing condensate fraction and a decrease of the chemical potential along the evolution from the BCS to the BEC limit. Our results agree quantitatively with numerical simulations and recent experimental data.