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.

翻译：我们考虑非局部部分差异方程式的数值解决方案,该方程式在含有单一光子的两层原子系统中模拟集体自发排放过程。我们重塑了这个问题,将其作为原子自由度的分化式正方程式,并描述高斯原子密度的高效解决方案。由集成配方产生的历史依赖问题通过耗资总和历史压缩来解决。我们展示了两种有物理意义的系统的解决办法:首先,最初的原子通过自发排放而衰变成光子,其次,光子脉冲被用于极富的原子,然后腐烂。