Robust stationary mechanical squeezing in a kicked quadratic optomechanical system

We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly stiffening the effective harmonic potential felt by the mechanical resonator. These "optical spring kicks" tend to squeeze the resonator position, and due to the interplay with fluctuation-dissipation processes one can generate a stationary state with more than 13 dB of squeezing even starting from moderately "pre-cooled" initial thermal states.