Superfluid properties of bright solitons in a ring

TL;DR

This paper theoretically explores superfluid properties of a one-dimensional ring superfluid, deriving a superfluid fraction formula, and analyzing how solitons and external potentials influence superfluid behavior and stability.

Contribution

It extends Leggett's superfluid fraction formula to ring geometries and investigates soliton formation, stability, and superfluidity under various conditions in a one-dimensional superfluid.

Findings

Superfluid fraction detects soliton emergence.

Soliton formation decreases superfluid fraction.

Critical velocity leads to superfluid fraction vanishing.

Abstract

We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.