In this paper, we propose two quantum optomechanical arrangements that permit the dissipationenabled generation of steady two-mode mechanical squeezed states. In the first setup, the mechanical oscillators are placed in a two-mode optical resonator while in the second setup the mechanical oscillators are located in two coupled single-mode cavities. We show analytically that for an appropriate choice of the pump parameters, the two mechanical oscillators can be driven by cavity dissipation into a stationary two-mode squeezed vacuum, provided that mechanical damping is negligible. The effect of thermal fluctuations is also investigated in detail and show that ground state pre-cooling of the oscillators in not necessary for the two-mode squeezing. These proposals can be realized in a number of optomechanical systems with current state-of-the-art experimental techniques.

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