  We study cavity quantum electrodynamics of Bose-condensed atoms that are
subjected to continuous monitoring of the light leaking out of the cavity. Due
to a given detection record of each stochastic realization, individual runs
spontaneously break the symmetry of the spatial profile of the atom cloud and
this symmetry can be restored by considering ensemble averages over many
realizations. We show that the cavity optomechanical excitations of the
condensate can be engineered to target specific collective modes. This is
achieved by exploiting the spatial structure and symmetries of the collective
modes and light fields. The cavity fields can be utilized both for strong
driving of the collective modes and for their measurement. In the weak
excitation limit the condensate-cavity system may be employed as a sensitive
phonon detector which operates by counting photons outside the cavity that have
been selectively scattered by desired phonons.
