Finding the stable mechanism of ring solitons in two-dimensional Fermi superfluids

TL;DR

This paper investigates the stability of ring solitons in two-dimensional Fermi superfluids, revealing how harmonic traps can stabilize them at specific positions and describing their oscillatory behavior and decay mechanisms.

Contribution

It introduces a theoretical framework using Bogoliubov-de Gennes equations to identify conditions for stable ring solitons in trapped Fermi superfluids, highlighting the role of curvature and trapping potential.

Findings

Ring solitons are driven to the system edge in uniform conditions.

Harmonic traps can stabilize ring solitons at specific equilibrium radii.

Dissipation leads to decay of ring solitons into sound ripples.

Abstract

We theoretically investigate the stable mechanism of a ring soliton in two-dimensional Fermi superfluids by solving the Bogoliubov-de Gennes equations and their time-dependent counterparts. In the uniform situation, we discover that the ring soliton is always driven away from its initial location, and moves towards the edge due to a curvature-induced effective potential. The ring soliton is impossible to remain static at any location in the uniform system. To balance the density difference between the ring soliton's two sides, a harmonic trap is introduced, which can exert an effect to counterbalances the curvature-induced effective potential. This enables the ring dark soliton to become a stable state at a particular equilibrium position r_s, where the free energy of the ring dark soliton just reaches the maximum value. Once ring soliton is slightly deviated from r_s, some stable periodic oscillations of ring soliton around r_s will turn out. Some dissipation will possibly occur to ring soliton once its minimum radius is comparable to the healing length of soliton's Friedel oscillation. This dissipation will increase the oscillation amplitude and finally make the ring soliton decay into sound ripples. Our research lays the groundwork for a more in-depth understanding of the stable mechanism of a ring dark soliton in the future.