▎ 摘　　要

We study the quantum dynamics of a nanomechanical graphene resonator. Neglecting the nonlinearities in the graphene membrane and applying a back-gate voltage, the vibrational state of the graphene membrane can be manipulated. We show that in the specific regime coherent states can be generated in the membrane. Moreover, the interaction between the vibrating graphene membrane and a Rydberg atom is investigated. This interaction originates from the Casimir-Polder interaction. Consequently, squeezed states or nonlinear coherent states may be generated in the membrane. Depending on the initial state of the graphene membrane, the membrane state may exhibit quadrature squeezing.