Maximal entanglement and switch squeezing with atom coupled to cavity field and graphene membrane

In this paper, we investigate the entanglement and squeezing dynamics of the system consisting of an atom coupled to a cavity field and the graphene membrane using dressed states. The effect of the atomic coherent angle on the time evolution of the entanglement and the quadrature squeezing is discussed. We show that the maximally entangled state between the atom and the mechanical resonator can be created. It is found that the entanglement between the atom and the cavity field increases with the increases in the coherent angle. We demonstrate how to switch from no squeezing to large squeezing by manipulating the initial state of an atom. Moreover, the periodic phonon field squeezed state with long time and high degree can be generated, which has a potential application in the field of high-precision measurement and quantum information processing.