Continuous wave solutions in spinor Bose-Einstein condensates

TL;DR

This paper derives and analyzes more general analytic continuous wave solutions for spinor Bose-Einstein condensates in a magnetic field, accounting for Zeeman effects and spin component differences, and examines their stability and spin mixing frequencies.

Contribution

It presents the first comprehensive analytic solutions for spinor BECs with different spin components and Zeeman effects, extending previous models.

Findings

Solutions include different chemical potentials and wavevectors for spin components.

Linear Zeeman effects can be gauged away, but quadratic effects alter solutions.

Stable fixed points and coherent spin mixing frequencies are identified.

Abstract

We find analytic continuous wave (cw) solutions for spinor Bose-Einstein condenates (BECs) in a magnetic field that are more general than those published to date. For particles with spin F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wavevectors of the different spin components are different from each other. We include linear and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field is constant and uniform, can be mathematically eliminated by a gauge transformation, but quadratic Zeeman effects modify the cw solutions in a way similar to non-zero differences in the wavenumbers between the different spin states. The solutions are stable fixed points within the continuous wave framework, and the coherent spin mixing frequencies are obtained.