吸收和放大介质中自发发射的费米黄金法则
Fermi's golden rule for spontaneous emission in absorptive and amplifying media
摘要：
我们证明了一个基本的故障的光子自发发射（SE）公式来自费米的黄金法则，在吸收和放大介质中，其中一个假设SE率标度与当地的光子态密度，一种方法经常使用在更复杂的，半经典的纳米光子学模拟。在任意线性介质的存在下，使用宏观麦克斯韦方程组的严格量子化，我们推导出一个修正的费米黄金法则和量子二能级系统（TLS）的主方程，产生一个量子泵浦项和修改后的衰减率是净正的。我们展示了严格的数值计算结果的TLS的时间动力学的两个耦合的微盘谐振器的例子，形成一个增益-损耗介质，并证明了明确的失败，通常采用的公式仅基于本地的状态密度。
英文摘要：
We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.
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