A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
Numerical Analysis
2023-07-10 v2 Numerical Analysis
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2109.06956,
title = {A fast, high-order numerical method for the simulation of single-excitation states in quantum optics},
author = {Jeremy Hoskins and Jason Kaye and Manas Rachh and John C. Schotland},
journal= {arXiv preprint arXiv:2109.06956},
year = {2023}
}