Bose-Einstein condensation with internal degrees of freedom in alkali atom gases

TL;DR

This paper extends Bogoliubov theory to Bose-Einstein condensates with internal degrees of freedom, analyzing their ground states, collective excitations, and potential for creating novel topological vortices in alkali atom gases.

Contribution

It introduces a generalized theoretical framework for BECs with internal states, including symmetry considerations and the prediction of new vortex types.

Findings

Ground state can break time reversal symmetry

Identification of low-lying spin and density wave modes

Proposal for experimental creation of novel vortices

Abstract

The Bogoliubov theory is extended to a Bose-Einstein condensation with internal degrees of freedom, realized recently in $^{23}$Na gases where several hyperfine states are simultaneously cooled optically. Starting with a Hamiltonian constructed from general gauge and spin rotation symmetry principles fundamental equations for condensate are derived. The ground state where time reversal symmetry is broken in some case and low-lying collective modes, e.g. spin and density wave modes, are discussed. Novel vortex as a topological defect can be created experimentally.