  We propose a scheme to prepare a macroscopic mechanical oscillator in a
catlike state, close to a coherent state superposition. The mechanical
oscillator, coupled by radiation-pressure interaction to a field in an optical
cavity, is first prepared close to a squeezed vacuum state using a reservoir
engineering technique. The system is then probed using a short optical pulse
tuned to the lower motional sideband of the cavity resonance, realizing a
photon-phonon swap interaction. A photon number measurement of the photons
emerging from the cavity then conditions a phonon-subtracted catlike state with
a negative Wigner distribution exhibiting separated peaks and multiple
interference fringes. We show that this scheme is feasible using
state-of-the-art photonic crystal optomechanical system.
