Entanglement characteristics of output optical fields in double-cavity optomechanics

Radiation pressure in an optomechanical system can be used to generate various quantum entanglements between the subsystems. Recently, one paid more attention to the study of quantum entanglement in an optomechanical system. Here in this work, we study the properties of output entanglement between two filtered output optical fields by the logarithmic negativity method in a double-cavity optomechanical system. Our calculations show that the decay rate of the mechanical resonator, the bandwidth of filter function, and non-equal-coupling will evidently affect the value of the output entanglement. In particular, under the parameters of equal-coupling and zero filter bandwidth, the output entanglement in the vicinity of resonant frequency (omega = 0 in the rotating frame) will decease with mechanical decay rate increasing. But under the parameters of equal-coupling and non-zero filter bandwidth, the output entanglement will be suppressed if the center frequency of output field is in the vicinity of the resonant frequency. However, the output entanglement can be enhanced if we adopt a non-equal-coupling to counteract the suppression effect of the filter bandwidth. Furthermore, we find that there are three peaks in the whole center frequency domain of the output field if we adopt strong non-equal-coupling. This is because the normal mode of Hamiltonian H-int will split into three normal modes in this case. Our results can also be used in other parametrically coupled three-mode bosonic systems and may be applied to realizing the state transfer process and quantum teleportation in an optomechanical system.