Entangled mechanical cat states via conditional single photon optomechanics

Abstract

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