Abstract
We present finite-difference time-domain schemes to numerically solve quantum Maxwell's equations for arbitrary inhomogeneous media based on the macroscopic theory on quantum electrodynamics. In the Heisenberg picture, quantum Maxwell dynamical operators are expanded by a set of ladder operators defined in the coordinate space while non-orthogonal basis corresponding to a new long-range propagators different from the classical Green's function. The proposed time-domain quantum Maxwell solver is useful to study the local nature of quantum information propagation such as virtual photons or near single photon sources. We provide numerical examples associated with two photon interference occurring in a quantum beam splitter, called Hong-Ou-Mandel effect. Moreover, we emulate the recent interesting experiment on quantum interference across an astronomical distance.
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