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In this paper, we propose two quantum optomechanical arrangements that permitthe dissipation-enabled generation of steady two-mode mechanical squeezedstates. In the first setup, the mechanical oscillators are placed in a two-modeoptical resonator while in the second setup the mechanical oscillators arelocated in two coupled single-mode cavities. We show analytically that for anappropriate choice of the pump parameters, the two mechanical oscillators canbe driven by cavity dissipation into a stationary two-mode squeezed vacuum,provided that mechanical damping is negligible. The effect of thermalfluctuations is also investigated in detail and show that ground statepre-cooling of the oscillators in not necessary for the two-mode squeezing.These proposals can be realized in a number of optomechanical systems withcurrent state-of-the-art experimental techniques.

Dissipation-driven two-mode mechanical squeezed states in optomechanical systems