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arXiv:2412.15357 · Optica Pura y Aplicada

Complete Rabi oscillations in the ion–laser interaction

Marco A. García-Márquez

Published Mar 31, 2025• 0 citations
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Abstract

We present the dynamics of a single harmonically trapped ion interacting with a laser, considering a linear combination of two eigenstates of the system as the initial state.The conditions on the physical parameters that allow for the evolution of the system are discussed.We are able to obtain analytical results using no other approximation than the optical rotating-wave approximation and are able to show Rabi oscillations for such initial states.

DOI
10.7149/opa.58.1.51192

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We present the dynamics of a single harmonically trapped ion interacting with a laser, considering a linear combination of two eigenstates of the system as the initial state.The conditions on the physical parameters that allow for the evolution of the system are discussed.We are able to obtain analytical results using no other approximation than the optical rotating-wave approximation and are able to show Rabi oscillations for such initial states.
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In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.
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.