杂质在单色光驱动下的准Stationary State特性Ⅰ--有效理论
Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light I - The Effective Theory
摘要：
考虑了在费米子热库环境中，由单色光驱动的杂质（$N$ -能级原子）。外部光源是原子哈密顿量的时间周期性扰动，其刺激两个原子能级$E_{1}$和$E_{N}$之间的跃迁，因此充当光泵。本工作的目的是分析复合系统的全微观时间演化所产生的有效原子动力学。我们证明，特别是，人口的原子动力学松弛大的时间到一个准稳态，也就是说，一个稳定的状态到小振荡驱动的外部光源。这个状态被证明是由一个平衡条件唯一决定的。后者与自发/受激发射/吸收速率的\textquotedblleft广义爱因斯坦关系\textquotedblright关系有关，它在概念上类似于爱因斯坦在1916年导出的唯象关系。作为应用，我们从量子力学的第一性原理表明如何反转的人口的能级的杂质在晶体中可以出现。我们的结果是基于谱分析的生成元的发展半群有关的非自治柯西问题有效地描述原子动力学。
英文摘要：
We consider an impurity ($N$--level atom) driven by monochromatic light in a host environment which is a fermionic thermal reservoir. The external light source is a time--periodic perturbation of the atomic Hamiltonian stimulating transitions between two atomic energy levels $E_{1}$ and $E_{N}$ and thus acts as an optical pump. The purpose of the present work is the analysis of the effective atomic dynamics resulting from the full microscopic time--evolution of the compound system. We prove, in particular, that the atomic dynamics of population relaxes for large times to a quasi-stationary state, that is, a stationary state up to small oscillations driven by the external light source. This state turns out to be uniquely determined by a balance condition. The latter is related to \textquotedblleft generalized Einstein relations\textquotedblright relations of spontaneous/stimulated emission/absorption rates, which are conceptually similar to the phenomenological relations derived by Einstein in 1916. As an application we show from quantum mechanical first principles how an inversion of population of energy levels of an impurity in a crystal can appear. Our results are based on the spectral analysis of the generator of the evolution semigroup related to a non--autonomous Cauchy problem effectively describing the atomic dynamics.
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