Rabi oscillations and Floquet states are likely the most familiar concepts associated with a periodically time-varying Hamiltonian. Here, we present an exactly solvable model of a two-level system coupled to both a continuum and a classical field that varies sinusoidally with time, which sheds light on the relationship between the two problems. For a field of the rotating-wave-approximation form, results show that the dynamics of the two-level system can be mapped exactly onto that for a static field, if one shifts the energy separation between the two levels by an amount equal to $\hslash \omega$, where ω is the frequency of the field and $\hslash$ is Planck's constant. This correspondence allows one to view Rabi oscillations and Floquet states from the simpler perspective of their time-independent-problem equivalents. The comparison between the rigorous results and those from perturbation theory helps clarify some of the difficulties underlying textbook proofs of Fermi's golden rule, and the discussions on quantum decay and linear response theory.

中文翻译：

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拉比振荡，弗洛奎特状态，费米的黄金法则，以及所有这些：来自完全可解的两层模型的见解

拉比振荡和浮球状态可能是与周期性时变哈密顿量相关的最熟悉的概念。在这里，我们提供了一个两级系统的精确可解模型，该模型与连续谱和经典场都耦合，该经典场随时间呈正弦变化，这为两个问题之间的关系提供了启示。对于旋转波近似形式的一个场，结果表明，如果将两个能级之间的能量分离移动一个等于的量，则两能级系统的动力学可以精确地映射到静态场上。$\hslash \omega$，其中ω是磁场的频率， $\hslash$是普朗克的常数。这种对应关系使人们可以从与时间无关的问题的等价物的更简单角度来观察拉比振荡和浮球状态。将严格结果与摄动理论的结果进行比较，有助于弄清费米黄金定律的教科书证明所基于的一些困难，以及有关量子衰减和线性响应理论的讨论。