Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

TL;DR

This paper numerically studies atomic Josephson vortices in two-component superfluids, revealing their dispersion relations, inertial mass behavior, and new solitary-wave excitations, with implications for understanding superfluid dynamics.

Contribution

It extends zero-velocity solutions to finite velocities, analyzes inertial mass divergence, compares with sine-Gordon solitons, and discovers a new solitary-wave branch in coupled superfluids.

Findings

Inertial mass depends on linear coupling and diverges at a critical point.

Low-velocity quasiparticles with negative inertial mass emerge at finite momentum.

A new solitary-wave branch exists with distinct stability properties.

Abstract

Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.