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

TL;DR

This paper introduces a fast, high-order numerical method for simulating single-excitation states in quantum optics, efficiently solving integro-differential equations modeling collective atomic emission.

Contribution

The authors develop an efficient solver for nonlocal PDEs in quantum optics, employing sum-of-exponentials history compression for improved computational performance.

Findings

Successfully simulates spontaneous emission dynamics

Accurately models photon-atom interactions

Demonstrates efficiency on physical systems

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.