Structure-preserving real-space quantum simulation of Maxwell fields in inhomogeneous photonic structures
Phys. Rev. A 114, 033508 – Published 8 September, 2026
DOI: https://doi.org/10.1103/2k9f-3256
Abstract
Quantum-optical simulations of inhomogeneous media typically rely on a global eigenmode basis that must be recomputed for each geometry. We show that, for lossless, nondispersive media, the dynamics can instead be formulated without such a basis. From the source-free Maxwell equations we identify a self-adjoint real-space generator of single-photon dynamics and directly construct bosonic field operators, a single-particle Hamiltonian, and a Liouville–von Neumann equation for the single-photon density matrix. A finite integration technique discretization transfers this operator structure to the numerical grid while preserving self-adjointness. This ensures unitary evolution and exact photon-number conservation up to projection accuracy and machine precision. Numerical examples demonstrate single-photon propagation in a dielectric waveguide and reproduce the two-photon Hong-Ou-Mandel dip in a 50-50 coupler. The few-photon dynamics in this formulation is fully determined by the bosonic symmetry of the state space and the linear single-particle propagation, without explicit photon-photon interaction terms. The approach therefore enables direct quantum-optical simulation of inhomogeneous and geometrically complex photonic structures.
