In this paper, we consider the generation of mechanical squeezed states and single-phonon Fock states, respectively, by homodyne detection and photon subtraction in a dissipative or dispersive optomechanical system under the situation that the cavity linewidth κc is much larger than the mechanical frequency ωm. We at first show that strong mechanical squeezing beyond the 3-dB limit can be achieved by homodyning the filtered cavity output field in a purely dispersive or purely dissipative optomechanical system for κc≫ωm, while the combinati...
