Non-Gaussian entanglement in an optomechanical system

The non-Gaussianity and entanglement in an optomechanical system with the dispersive coupling is theoretically considered for the coherent optical and vacuum mechanical input. The so-called non-Gaussianity is evaluated as a function of the modulus of coherent state parameter of the input optical field and the normalized optomechanical coupling constant. To detect and quantify the entanglement in the system, three criteria (a criterion based on the trace of the reduced density matrix squared, the Simon criterion, and that suggested by Shchukin and Vogel) are used. The results of application of these criteria are compared and critically analyzed. The situations in which these criteria agree among each other and in which they disagree are rationalized. An important conclusion of the work is that, in the regime of strong optomechanical coupling, the non-Gaussian entanglement in the system should be ascribed to the correlations of an exponentially high order.