Two-fluid model of a Bose-Einstein condensate in the cavity optomechanical regime*

We analyze an atomic Bose-Einstein condensate trapped in a high-$Q$ optical cavity driven by a feeble optical field. The dynamics of the resulting collective density excitation of the condensate are formally analogous to the central model system of cavity optomechanics: a radiation pressure driven mechanical oscillator [Brennecke {\it et al}., Science \textbf{322}, 235 (2008)]. However, although BEC-based optomechanical systems have several desirable properties, one must also take into account the effect of atom-atom interactions. We treat these interactions via a two-fluid model that retains the intuitive appeal of the non-interacting two-mode description. We find that the Bogoliubov excitation spectrum of this system comprises a gapped upper branch and a lower branch that can include an unstable excitation mode. \\[4pt] D. S. Goldbaum, K. Zhang and P. Meystre, {\it Two-fluid model of a Bose-Einstein condensate in the cavity optomechanical regime}, arXiv:0911.3234.