  Recognized as a potential resource for quantum technologies and a possible
testbed for fundamental physics, the control and preparation of nonclassical
states of mechanical oscillators has been explored extensively. Within
optomechanics, quantum state synthesis can be realized by entangling photonic
and phononic degrees of freedom followed by optical detection. Single-photon
detection enables one of the most powerful forms of such heralded quantum state
preparation, permitting the creation of single phonon states when applied to
conventional cavity optomechanical systems. As the complexity of optomechanical
systems increases, single-photon detection may provide heralded access to a
larger class of exotic quantum states. Here, we examine the quantum dynamics of
optomechanical systems that permit forward Brillouin scattering, where a single
phonon mode mediates transitions between a collection of equally spaced optical
resonances. Solving both the Schrodinger equation and the Lindblad master
equation for this system, we find that initial states comprised of single
photons or weak laser pulses evolve into complex quantum states where the
frequency of single photon states and the phonon occupation number are
entangled. Physically, these interactions permit a single photon to scatter to
lower frequencies, where phonon excitation occurs for each scattering event.
Combining this result with frequency filtering, we show how single-photon
detection can herald selected multi-phonon Fock states, even in the presence of
optical losses. We also present an approach for quantum tomography of the
heralded phonon states.
