Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases

TL;DR

This paper explores the local spin-gauge symmetry in Bose-Einstein condensates of atomic gases, revealing how it influences superfluid velocity, energy level degeneracy, and vortex states in static versus dynamic traps.

Contribution

It introduces the concept of spin-gauge symmetry in spinor BECs and analyzes its effects on vortex formation and energy level splitting in different trapping conditions.

Findings

Superfluid velocity arises from Berry phase effects.

Degeneracy of harmonic energy levels is split in static traps.

Vortex ground states can form due to symmetry breaking.

Abstract

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity ${\bf u}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static" traps, ${\bf u}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\bf \Omega}_{c1}$, and can lead to {\em vortex ground states}. The inversion symmetry of ${\bf \Omega}_{c1}$, however, is not broken in ``dynamic" traps. Rotations of the atom cloud can be generated by adiabatic effects without physically rotating the entire trap.