Vacuum Induced Transparency, Vacuum Rabi Splitting, and Exceptional Points in a Quantum Emitter Near a Graphene Nanodisk

Abstract

This work studies the absorption spectrum of a two-level quantum emitter coupled to a photonic environment modified by the plasmon modes of a graphene nanodisk. Using macroscopic quantum electrodynamics and a Lorentzian mapping, the system is described within an effective cavity quantum electrodynamics framework. Analytical expressions are derived for the linear susceptibility, and three distinct spectral regimes are identified. In vacuum induced transparency, destructive quantum interference opens a narrow transparency window in the absorption spectrum. In vacuum Rabi splitting, coherent energy exchange between the emitter and the plasmonically modified photonic mode produces a well-resolved doublet. When plasmon losses are large, the required interference is suppressed, leading to the absence of induced optical transparency. It is shown that the transitions between these regimes are strictly determined by the exceptional points of the system's effective non-Hermitian Hamiltonian, and a complete phase diagram is provided as a function of the emitter-nanodisk distance and the free-space decay rate. The results highlight graphene nanodisks as a highly tunable platform for the dynamic control of quantum interference, offering potential applications in reconfigurable nanophotonic spectral switching and transparency-window engineering.