Low energy dynamics of spinor condensates

TL;DR

This paper derives a low energy Lagrangian for the spin dynamics in spinor Bose condensates with zero average magnetization, extending previous models to all phases except ferromagnetic ones.

Contribution

It provides a sigma model-based Lagrangian for spin dynamics applicable to multiple phases of spinor condensates, excluding ferromagnetic phases.

Findings

Derived the low energy Lagrangian for spinor condensates.

Extended the sigma model description to various phases.

Clarified the dynamics in non-ferromagnetic phases.

Abstract

We present a derivation of the low energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate, for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet, for which the low energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas.