A fast, high-order numerical method for the simulation of single-excitation states in quantum optics

• DOI: 10.1016/j.jcp.2022.111723
• Publication Date: 2022-10-26T15:25:18Z
• Authors: Jeremy G. Hoskins; Jason Kaye; Manas Rachh; John C. Schotland
• Keywords: G.1.9; Quantum Physics; G.1.8; G.1.9; 45D05, 35Q40, 81-08; G.1.8; FOS: Mathematics; FOS: Physical sciences; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 0101 mathematics; Quantum Physics (quant-ph); 01 natural sciences

We consider the numerical solution of a nonlocal partial differential equation which models the process of collective spontaneous emission in a two-level atomic system containing a single photon. We reformulate the problem as an integro-differential equation for the atomic degrees of freedom, and describe an efficient solver for the case of a Gaussian atomic density. The problem of history dependence arising from the integral formulation is addressed using sum-of-exponentials history compression. We demonstrate the solver on two systems of physical interest: in the first, an initially-excited atom decays into a photon by spontaneous emission, and in the second, a photon pulse is used to an excite an atom, which then decays.