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arXiv · 1709.00624

A simple, analytic solution of the Rabi model using multiple-scales

Luis Octavio Castanos Cervantes
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Abstract

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.

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Luis Octavio Castanos Cervantes. 2017-11-30. A simple, analytic solution of the Rabi model using multiple-scales. https://arxiv.org/abs/1709.00624

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