  We analyze an atomic Bose-Einstein condensate trapped in a high-Q optical
cavity driven by a feeble optical field, a situation formally analogous to the
central paradigm of cavity optomechanics [Brennecke et al., Science, 322, 235
(2008)]. We account for two-body interactions via a two-fluid model that
retains the intuitive appeal of the optomechanical two-mode description. The
Bogoliubov excitation spectrum of this system comprises a gapped upper branch
and a lower branch that can include an unstable excitation mode.
