Diffused vorticity and moment of inertia of a spin-orbit coupled Bose-Einstein condensate

TL;DR

This paper develops a hydrodynamic theory for spinor superfluids with spin-orbit coupling, revealing diffused vorticity and analyzing the moment of inertia behavior in different coupling regimes.

Contribution

It introduces a hydrodynamic framework for spinor superfluids with spin-orbit coupling and explores their rotational properties and moment of inertia.

Findings

Velocity field exhibits diffused vorticity unlike traditional superfluids.

Moment of inertia reaches rigid body value at specific phase transitions.

Raman and Rashba spin-orbit couplings influence the rotational behavior.

Abstract

By developing the hydrodynamic theory of spinor superfluids we calculate the moment of inertia of a harmonically trapped Bose-Einstein condensate with spin-orbit coupling. We show that the velocity field associated with the rotation of the fluid exhibits diffused vorticity, in contrast to the irrotational behavior characterizing a superfluid. Both Raman-induced and Rashba spin-orbit couplings are considered. In the first case the moment of inertia takes the rigid value at the transition between the plane wave and the single minimum phase, while in the latter case the rigid value is achieved in the limit of isotropic Rashba coupling. A procedure to generate the rigid rotation of the fluid and to measure the moment of inertia is proposed. The quenching of the quantum of circulation $h/m$, caused by Raman induced spin-orbit coupling in a toroidal geometry, is also discussed.