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首页> 外文期刊>Annales Henri Poincare >Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light I: The Effective Theory
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Characterization of the Quasi-Stationary State of an Impurity Driven by Monochromatic Light I: The Effective Theory

机译：单色光驱动的杂质的准平稳状态的表征I：有效理论

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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 "generalized Einstein 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.
机译：我们考虑了在宿主环境中由单色光驱动的杂质（N级原子），该环境是铁离子热库。外部光源是在两个原子能级E _1和E _N之间的原子哈密顿量刺激跃迁的时间周期扰动，因此起着光泵的作用。本工作的目的是分析由复合系统的整个微观时间演化产生的有效原子动力学。我们特别证明了，原子的原子动力学在很大程度上弛豫到了准平稳状态，也就是从外部光源驱动的直至小振荡的稳态。证明该状态由平衡条件唯一地确定。后者与自发/受激发射/吸收速率的“广义爱因斯坦关系”有关，在概念上类似于爱因斯坦在1916年推导的现象学关系。晶体中杂质的含量会出现。我们的结果基于与非自治柯西问题有关的演化半群生成器的频谱分析，该问题有效地描述了原子动力学。

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