# Crossover between snake instability and Josephson instability of dark solitons in superfluid Fermi gases

## TL;DR

This paper investigates the decay mechanisms of dark solitons in superfluid Fermi gases, revealing a crossover from snake instability in the BEC regime to Josephson instability in the BCS regime, with distinct underlying physical processes.

## Contribution

It demonstrates a qualitative difference between soliton decay in BEC and BCS regimes using simulations and analysis, highlighting a crossover in decay mechanisms.

## Key findings

- In BEC regime, amplitude fluctuations induce snaking deformations.
- In BCS regime, phase fluctuations lead to Josephson currents destroying the soliton.
- The decay mechanisms are experimentally distinguishable.

## Abstract

Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC- and BCS-regimes. On the BEC-side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS-side, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents. The latter mechanism is qualitatively different from the snaking instability and this difference should be experimentally detectable.