  We describe an optomechanical system in which the mean phonon number of a
single mechanical mode conditionally displaces the amplitude of the optical
field. Using homodyne detection of the output field we establish the conditions
under which phonon number quantum jumps can be inferred from the measurement
record: both the cavity damping rate and the measurement rate of the phonon
number must be much greater than the thermalization rate of the mechanical
mode. We present simulations of the conditional dynamics of the measured system
using the stochastic master equation. In the good-measurement limit, the
conditional evolution of the mean phonon number shows quantum jumps as phonons
enter and exit the mechanical resonator via the bath.
