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.

中文翻译：

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一种用于模拟量子光学中单激发态的快速、高阶数值方法

我们考虑非局部偏微分方程的数值解，该方程模拟包含单个光子的两能级原子系统中的集体自发发射过程。我们将问题重新表述为原子自由度的积分微分方程，并描述了高斯原子密度情况下的有效求解器。积分公式引起的历史依赖问题使用指数和历史压缩来解决。我们在两个物理感兴趣的系统上演示求解器：在第一个中，最初激发的原子通过自发发射衰变成光子，在第二个中，使用光子脉冲激发原子，然后原子衰变。