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In this study, we explore the behavior of a solid-state resonator composed of a material with third-order nonlinearity. Specifically, we examine the interaction between a quantum dot and non-classical light, with a focus on the effects of self-phase modulation. This involves analyzing how a non-classical pump field interacts with a quantum dot within a nonlinear medium. To better understand this interaction, we describe the excitation of a quantum well and the formation of an exciton using a two-level model that takes into account the nonlinear medium and the interaction with the quantum field. Previous research has examined the Schrodinger equation for the field and exciton subsystems without detuning.