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arXiv · 2109.06956

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

Jeremy Hoskins·Jason Kaye·Manas Rachh·John C. Schotland
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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.

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Jeremy Hoskins, Jason Kaye, Manas Rachh, John C. Schotland. 2021-09-14. A fast, high-order numerical method for the simulation of single-excitation states in quantum optics. https://doi.org/10.1016/j.jcp.2022.111723

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