Radiative coupling and decay dynamics of two two-level quantum emitters in arbitrary dielectric nanostructures

Photon-mediated coherent interaction determines the decay dynamics of quantum emitters and facilitates on-chip quantum manipulation for quantum information processing. We derive a general formalism to efficiently and flexibly simulate the radiative coupling between two two-level quantum emitters in arbitrary dielectric nanostructures, based on which, the decay dynamics of the two quantum emitters can be obtained. We demonstrate this formalism to investigate the two quantum dots embedded in the photonic crystal L3 cavity. The anticrossing behavior in the evolution spectrum and the vacuum Rabi oscillation in the populations of the two quantum dots can be simulated in both zero and small dot-dot detuning case. Our formalism can serve as a flexible and efficient theoretical tool and may be further developed to handle the cases for different initial states, multiple quantum emitters, and arbitrary metallic nanostructures.