Conserving Gapless Mean-Field Theory of a Multi-Component Bose-Einstein Condensate

TL;DR

This paper introduces a mean-field theory for spin-1 Bose-Einstein condensates that accurately describes thermodynamics and excitation spectra, revealing a single gapless mode contrary to previous predictions.

Contribution

It develops a gapless mean-field framework for multi-component BECs that satisfies conservation laws and the Hugenholtz-Pines theorem, improving upon prior models.

Findings

Condensate remains in the same internal state up to T_c.

Antiferromagnetic and ferromagnetic interactions show only one gapless excitation mode.

Contradicts Bogoliubov theory predictions of multiple gapless modes.

Abstract

We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.