Rabi oscillations, Floquet states, Fermi's golden rule, and all that: Insights from an exactly solvable two-level model

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 hco, where co is the frequency of the field and h 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. (C) 2021 Author(s).

Automated summary

Rabi oscillations and Floquet states are discussed within the context of a periodically time-varying Hamiltonian, using an exactly solvable model of a two-level system coupled to both a continuum and a classical field. The study reveals the relationship between the two concepts and shows that the dynamics of the two-level system can be mapped onto a static field by adjusting the energy separation between levels. Comparison between rigorous results and perturbation theory helps clarify difficulties in textbook proofs related to Fermi's golden rule, quantum decay, and linear response theory.