Snake instability of dark solitons in fermionic superfluids

TL;DR

This paper investigates the snake instability of dark solitons in fermionic superfluids across the BEC-BCS crossover using numerical simulations, revealing how the instability varies and is suppressed in different regimes.

Contribution

It provides a comprehensive numerical analysis of the snake instability in Fermi superfluids, linking theoretical predictions with experimental observations across the crossover.

Findings

Snaking behavior varies across the BEC-BCS crossover.

Decay into sound dominates in the deep BCS regime.

Discrepancy observed between numerical critical wavenumber and experiments at unitarity.

Abstract

We present numerical calculations of the snake instability in a Fermi superfluid within the Bogoliubov-de Gennes theory of the BEC to BCS crossover using the random phase approximation complemented by time-dependent simulations. We examine the snaking behaviour across the crossover and quantify the timescale and lengthscale of the instability. While the dynamic shows extensive snaking before eventually producing vortices and sound on the BEC side of the crossover, the snaking dynamics is preempted by decay into sound due to pair breaking in the deep BCS regime. At the unitarity limit, hydrodynamic arguments allow us to link the rate of snaking to the experimentally observable ratio of inertial to physical mass of the soliton. In this limit we witness an unresolved discrepancy between our numerical estimates for the critical wavenumber of suppression of the snake instability and recent experimental observations with an ultra-cold Fermi gas.