Bose-Einstein Condensation with Internal Degrees of Freedom in Alkali Atom Gases

TLDR

The Bogoliubov theory is extended to Bose‑Einstein condensates with internal degrees of freedom, as recently realized in 23Na gases where multiple hyperfine states are simultaneously cooled optically. Using a Hamiltonian built from general gauge and spin‑rotation symmetry principles, the authors derive the fundamental equations governing the condensate. The study finds that the ground state can break time‑reversal symmetry, low‑lying collective modes including spin and density waves arise, and a novel vortex topological defect can be experimentally created.

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.