Abstract
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 ℏω, where ω is the frequency of the field and ℏ 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.
Highlights
Rabi oscillations arise when a few-level quantum system is subjected to a periodically time-varying field
For a field of the rotating-waveapproximation 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 hx, where x is the frequency of the field and h is Planck’s constant
Students interested in these topics may fail to grasp the connection between Rabi oscillations and Floquet states beyond the obvious fact that they both involve a timevarying field. They may struggle to find pedagogical accounts in the literature discussing the effects of dissipation19 and spontaneous decay, which are central to the interpretation of many physical phenomena. They may ponder about the question as to how Rabi oscillations and Floquet states relate to results of time-dependent perturbation theory, and to linear response theory and Fermi’s golden rule
Summary
Rabi oscillations arise when a few-level quantum system is subjected to a periodically time-varying field. Students interested in these topics (and researchers from other disciplines) may fail to grasp the connection between Rabi oscillations and Floquet states beyond the obvious fact that they both involve a timevarying field Important, they may struggle to find pedagogical accounts in the literature discussing the effects of dissipation and spontaneous decay, which are central to the interpretation of many physical phenomena. They may struggle to find pedagogical accounts in the literature discussing the effects of dissipation and spontaneous decay, which are central to the interpretation of many physical phenomena They may ponder about the question as to how Rabi oscillations and Floquet states relate to results of time-dependent perturbation theory, and to linear response theory and Fermi’s golden rule. The equivalence between the two problems is closely related to the transformation from a stationary to a rotating frame used in nuclear magnetic resonance and atomic physics problems. a result derived from the RWA, we emphasize the fact that this correspondence is applicable to actual physical situations since the RWA is an excellent approximation near resonant conditions, that is, H % 0.22
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