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

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¹Department of Physics, Hokkaido University, Sapporo 060-0810

Received July 31, 2006; Accepted December 20, 2006; Published February 13, 2007

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.

https://doi.org/10.1143/JPSJ.76.024008

KEYWORDS: Bose–Einstein condensation, mean-field theory, spinor BEC, Luttinger–Ward functional, Bogoliubov–de Gennes equation

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

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