Abstract
This paper studies the dynamic effects of the driven external classical field on a system consists of a single two-level atom that interacted locally with a vibrating graphene membrane and a cavity field. The temporal wave function containing the tripartite interaction statuses via a canonical transformation and new resonance conditions is obtained. The possibility of studying the optimal behaviour of the quantum coherence and non-classicality for the graphene-field, atom-field, and atom-graphene states are investigated. It is found that the upper and lower bounds of the two phenomena depend on the detuning parameter, coupling strength of atom-graphene interaction, and initial atomic state. Based on the support of numerical computations, we demonstrate how to control the quantum system by the vibrating graphene membrane and the driven classical field.