▎ 摘　　要

In this paper, we study optical bistability (OB) and optical multistability (OM) in a defect medium with a monolayer of graphene quantum system. The graphene quantum system interacts with two weak probe laser fields and an elliptical polarized coupling beam for adjusting the linear and nonlinear optical properties of defect layer. We find that by controlling the relative phase between applied lights and elliptical parameter of the coupling light, the enhanced Kerr nonlinearity with probe amplification can be obtained in resonance of probe light. Then we study the transmission and reflection coefficients of the incident lights for controlling the OB and OM features of transmitted and reflected light beams, respectively. Also, we discuss the thickness effect of the defect layer on the OB and OM properties and find that the switching from OB to OM or vice versa is possible. Moreover, we realize that by modifying the nonlinear properties of the defect medium, one can control the behaviors of the OB and OM, respectively.