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

• URL: http://arxiv.org/abs/2109.06956v2
• Date: Thu, 6 Oct 2022 18:38:36 GMT
• Title: A fast, high-order numerical method for the simulation of single-excitation states in quantum optics
• Authors: Jeremy Hoskins and Jason Kaye and Manas Rachh and John C. Schotland
• Abstract summary: 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. 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 excite an atom, which then decays.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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