Quantum mechanical solution to spectral lineshape in strongly-coupled atom-nanocavity system

The strongly coupled system composed of atoms, molecules, molecule aggregates, and semiconductor quantum dots embedded within an optical microcavity/nanocavity with high quality factor and/or low modal volume has become an excellent platform to study cavity quantum electrodynamics (CQED), where a prominent quantum effect called Rabi splitting can occur due to strong interaction of cavity-mode single-photon with the two-level atomic states. In this paper, we build a new quantum model that can describe the optical response of the strongly-coupled system under the action of an external probing light and the spectral lineshape. We take the Hamiltonian for the strongly-coupled photon-atom system as the unperturbed Hamiltonian \bmH₀ and the interaction Hamiltonian of the probe light upon the coupled-system quantum states as the perturbed Hamiltonian \bmV. The theory yields a double Lorentzian lineshape for the permittivity function, which agrees well with experimental observation of Rabi splitting in terms of spectral splitting. This quantum theory will pave the way to construct a complete understanding for the microscopic strongly-coupled system that will become an important element for quantum information processing, nano-optical integrated circuits, and polariton chemistry.