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Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir

We study theoretically a three-mode optomechanical system where two mechanical oscillators are independently coupled to a single cavity mode. By optimized two-tone or four-tone driving of the cavity one can prepare the mechanical oscillators in an entangled two-mode squeezed state, even if they start in a thermal state. The highly-pure, symmetric steady-state achieved allows the optimal fidelity of standard continuous-variable teleportation protocols to be achieved. In contrast to other reservoir engineering approaches to generating mechanical entanglement, only a single reservoir is required to prepare the highly-pure entangled steady-state, greatly simplifying experimental implementation. The entanglement may be verified via a bound on the Duan inequality obtained from the cavity output spectrum. A similar technique may be used for the preparation of a highly-pure two-mode squeezed state of two cavity modes, coupled to a common mechanical oscillator.