Moving solitons in a one-dimensional fermionic superfluid

TL;DR

This paper develops an exact analytical theory for moving solitons in a one-dimensional fermionic superfluid, revealing their properties, stability criteria, and nonlinear dynamics within the Bogoliubov-de Gennes framework.

Contribution

It provides the first exact solution for traveling solitons in 1D fermionic superfluids using the Bogoliubov-de Gennes equations in the Andreev approximation.

Findings

Solitons exhibit a kink-like order parameter profile with Andreev bound states.

The phase jump and energy of the soliton decrease with velocity, vanishing at the Landau critical velocity.

The inertial mass of the soliton is much larger than its gravitational mass, affecting its dynamics.

Abstract

A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov-de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kink-like profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The "inertial" and "gravitational" masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent to the observed behavior of a soliton-like texture in related experiments in cold fermion gases [T. Yefsah et al., Nature 499, 426, (2013)]. Furthermore, we calculate the full non-linear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong non-linearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the non-linear soliton spectrum in superfluids.