Strong squeezing via phonon mediated spontaneous generation of photon pairs

We propose a scheme for generating squeezed light by using a double-cavity optomechanical system driven by a blue detuned laser in one cavity and by a red detuned laser in the other. This double-cavity system is shown to effectively mimic an interaction that is similar to the one for a downconverter, which is known to be a source of strong squeezing for light fields. There are however distinctions, as the phonons which lead to such an interaction can contribute to the quantum noise. We show that squeezing of the output fields, of the order of 10 dB, can be achieved even for an effective mechanical mode occupation number of about 4, which for the chosen parameters corresponds to 10 mK. Our results are generic and applicable to a wide class of electromechanical and optomechanical systems involving the interaction of two electromagnetic modes and one mechanical mode.