  In this paper, we propose two quantum optomechanical arrangements that permit
the dissipation-enabled 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.
