Entangled mechanical cat states via conditional single photon optomechanics

We study single photon optomechanics conditioned on photon counting events. By selecting only detection events that occur long after a photon pulse arrives at the cavity, the optomechanical interaction time can be increased, allowing a large momentum kick to be applied to the oscillator. We apply this to two optomechanical cavities set-up within a Mach-Zhender interferometer driven by a single photon source. The conditional state of the mechanical modes in such a system becomes an entangled cat state for detection times resulting in maximum mechanical amplitude in phase space. Further we study the dynamics induced by a second photon pulse injected into an already conditioned optomechanical cavity, a quarter of a mechanical period after the first photon has been detected. We illustrate how the optomechanical interaction resulting from the second photon can be strongly suppressed allowing conditional optomechanical routing of single photons with single photon control pulses.