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Physics Letters A

A simple, analytic solution of the semiclassical Rabi model in the red-detuned regime

Luis Octavio Castaños-Cervantes

Published Apr 2, 2019• 5 citations
Publisher
DOI
10.1016/j.physleta.2019.03.039

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We considered the semiclassical Rabi model, that is, a two-level system interacting with a single-mode, classical field. In resonance and for an arbitrary initial state of the system, we obtained a simple, approximate, and analytic solution that takes into account the counterrotating terms and that is accurate as long as the Rabi frequency is smaller than or equal to 1/2 (1/4) of the angular frequency of the field and 1 (10) Rabi oscillations are considered. In addition, the approximate solution has the same level of complexity as that obtained with the rotating-wave-approximation (RWA) and allows one to describe the evolution of the Bloch vector of the system in terms of a \textit{slow-precessional} and a \textit{fast-nutational} motion similar to that of a symmetric top with one point fixed. Finally, the approximate solution also leads to a simple criterion that allows one to determine the accuracy of the solution in the RWA.
We study the resonance-enhanced multiphoton ionization (REMPI) of atoms by intense, short, XUV radiation fields. To characterize Rabi oscillations and the resulting Autler-Townes doublet in the photoelectron spectrum, a minimal-state effective description is utilized, incorporating energy-level shifts, multiphoton couplings, and irreversible losses. Extending the semiclassical Rabi model with such higher-order terms, the complex population amplitudes of the Rabi cycling atom are found in simple analytic forms. This allows for the exact analytic evaluation of the photoelectron spectrum under various simultaneous physical effects. The origins of the spectral characteristics, such as the splitting, shifting, asymmetry, and multipeak pattern, are identified through the found spectrum formula. Furthermore, the dependence of these features on the field intensity, frequency detuning, and interaction time are analyzed in detail. Finally, as the simplicity of the spectrum formula is preserved when further higher-order light-matter interaction terms are added, the presented general framework is suitable for studying arbitrary ( n + m ) photon REMPI phenomena.