Spectrum and entanglement of phonons in quantum fluids of light

We study the quantum state of phonons propagating on top of a fluid of light coherently generated in a planar microcavity device by a quasiresonant incident laser beam. In the steady state under a monochromatic pump, because of the finite radiative lifetime of photons, a sizable incoherent population of low-frequency phonons is predicted to appear. Their mean occupation number differs from a Planck distribution and is independent of the photon lifetime. When the photon fluid is subjected to a sudden change of its parameters, additional phonon pairs are created in the fluid with remarkable two-mode squeezing and entanglement properties. Schemes to assess the nonseparability of the phonon state from measurements of the correlation functions of the emitted light are discussed.