Generation of two-mode squeezing of mechanical oscillators in the multi-mode optomechanical systems

We investigate the generation of two-mode mechanical squeezing in the multi-mode optomechanical systems with N mechanical oscillators. The cavity field is driven by an external field with time-varying amplitude. It is shown that the two-mode squeezed states of two arbitrary oscillators can be generated for an appropriate choice of the driving field. Our results show that the stronger squeezing can be achieved by increasing the driving field amplitude and enhancing the coupling between the mechanical oscillators and cavity field. In the addition, we find that the mechanical squeezed states are also affected by the number of mechanical oscillators: the more the mechanical oscillators, the larger the strength of squeezing.