  We present a theoretical study of an experiment designed to detect radiation
pressure shot noise in an optomechanical system. Our model consists of a
coherently driven optical cavity mode that is coupled to a mechanical
oscillator. We examine the cross-correlation between two quadratures of the
output field from the cavity. We determine under which circumstances radiation
pressure shot noise can be detected by a measurement of this cross-correlation.
This is done in the general case of nonzero detuning between the frequency of
the drive and the cavity resonance frequency. We study the qualitative features
of the different contributions to the cross-correlator and provide quantitative
figures of merit for the relative importance of the radiation pressure shot
noise contribution to other contributions. We also propose a modified setup of
this experiment relevant to the "membrane-in-the-middle" geometry, which
potentially can avoid the problems of static bistability and classical noise in
the drive.
