We condition the interaction of a single photon in an interferometer with two optomechanical systems. Conditioning on long detection times of the photon from the composite system results in an entangled mechanical cat state.
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.
The realization of multimode optomechanical interactions in the single-photon strong-coupling regime is a desired task in cavity optomechanics, but it remains a big challenge in realistic physical systems. In this work we propose a reliable scheme to simulate a three-mode optomechanical system working in the single-photon strong-coupling regime based on the Fredkin-type interaction. This is achieved by utilizing two strong drivings to the two exchange-coupled modes in the Fredkin-type coupling involving one optical mode and two mechanical-like modes. As an application of this enhanced three-mode nonlinear optomechanical coupling, we show how to generate entangled cat states of the mechanical-like modes using the conditional displacement mechanism. The quantum coherence effects in the generated states are investigated by calculating the two-mode joint Wigner function and quantum entanglement. The influence of the system dissipation on the state generation is also considered. This work will open up a different route to the study of multimode optomechanical interactions at the single-photon level.
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated optomechanical system (OMS), which is originally in the weak-coupling regime. The mechanical spring constant and optomechanical interaction are modulated periodically. This leads to the result that the resonant optomechanical interaction can be effectively enhanced into the single-photon strong-coupling regime by the modulation-induced mechanical parametric amplification. Moreover, the amplified phonon noise can be suppressed completely by introducing a squeezed vacuum reservoir, which ultimately leads to the realization of photon blockade in a weakly coupled OMS. The reached nonlinear quantum regime also allows us to engineer the nonclassical states (e.g., Schr\"odinger cat states) of the cavity field, which are robust against the phonon noise. This work offers an alternative approach to enhance the quantum nonlinearity of an OMS, which should expand the applications of cavity optomechanics in the quantum realm.