Simulating quantum emitters in arbitrary photonic environments using FDTD: beyond the semi-classical regime

We propose a numerical algorithm that integrates quantum two-level systems (TLSs) into the finite-difference time-domain (FDTD) framework for simulating quantum emitters in arbitrary 3D photonic environments. Conventional methods struggle with these systems due to their semi-classical nature and spurious self-interactions that arise when a TLS is driven by its own radiation field. We address these issues by determining the correct electric field for driving the TLS, as well as the current source used in FDTD for modeling photon emission. Our method, focusing on single-excitation states, employs a total field-incident field (TF-IF) technique to eliminate self-interactions, enabling precise simulations of photon emission and scattering. The algorithm also successfully models complex phenomena such as resonant energy transfer, superradiance, and vacuum Rabi splitting. This powerful computational tool is expected to substantially advance research in nanophotonics, quantum physics, and beyond.