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International Conference Laser Optics (ICLO)

One step beyond the RWA: a way to obtain precise polarization spectra without having to consider high-frequency density matrix fluctuations

A. G. Antipov, N. I. Matveeva, S. A. Pulkin, С. В. Савельева, Svetlana Uvarova, Вера Ивановна Яковлева

Published Jun 20, 2022• 0 citations
Publisher

Abstract

The method to improve the traditional rotating wave approximation in solving density matrix equation is proposed. We use the additional transformation to obtain more close approach to an exact solution than the usual rotating wave approximation. The proposed method is illustrated by the example of a two-level system driven by a polychromatic field.

DOI
10.1109/iclo54117.2022.9840178

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The method to improve the traditional rotating wave approximation in solving density matrix equation is proposed. We use the additional transformation to obtain more close approach to an exact solution than the usual rotating wave approximation. The proposed method is illustrated by the example of a two-level system driven by a polychromatic field.
Polarization spectra of a two-level system in a polychromatic field were obtained in two cases: using the rotating wave approximation and without using this approximation. The obtained spectra were compared using two indicators: the average deviation across the entire frequency range and the deviation at the transition frequency. Both indicators allow quantitative assessment of the distortion in polarization spectra introduced by the application of the rotating wave approximation. The dependencies of the above indicators on key model parameters were obtained – on the central frequency, detuning, and spectral width of the applied polychromatic field. The obtained dependencies allow evaluating the applicability limits of the rotating wave approximation for a given level of acceptable distortions in the polarization spectrum.
Abstract The impact of a polychromatic field on a two-level medium is considered in the limit of small amplitudes. In the indicated limit, we obtained asymptotic expansions of the polarization spectra of an arbitrary order of smallness. These polarization spectra were compared with the results of the numerical solution of the density matrix equation. Compared to numerical calculation methods, the asymptotic expansion offers an analytical estimation of the contribution of each individual component of a polychromatic field and a description of the intermode interaction. However, with an increase in the intensity of the driving field, the computational efficiency of the method decreases, since, to achieve the required accuracy, it is necessary to increase the order of the asymptotic expansion.