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Optics and Spectroscopy

Asymptotic Expansion of the Polarization Spectrum of a Two-Level System in a Polychromatic Field in the Small-Amplitude Limit

A. G. Antipov, S. A. Pulkin, Svetlana Uvarova

Published Aug 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x19080046

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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.
A two-level media driven by a polychromatic field is considered in the limit of small amplitudes. In this limit the asymptotic expansions for the polarization spectra of an arbitrary order are obtained. The obtained polarization spectra were compared with the numerical solution of the density matrix equation. Compared to numerical methods, the asymptotic expansion allows analytically estimating the contribution of each individual component of the polychromatic field and describing the intermode interaction. However, as the intensity of the acting field grows, the computational efficiency of the method decreases and to achieve the required accuracy it is necessary to increase the order of the asymptotic expansion.
An analytic expression of the polarization induced by a polychromatic weak probe field in a two-level medium, driven by a strong polychromatic pumping field, is obtained. This expression allows one to obtain both the absorption and dispersion spectra at any frequency of a probe field. The numerically calculated graphs of the central-component probe-field absorption and dispersion spectra, depending on the pumping-field amplitude in the cases of the one-, two- three-, four-, and five-component pumping field, are presented. It is shown that when the probe-field detuning is close to the strong-field Rabi frequency, the absorption spectrum changes to the dispersionlike form, while the dispersion spectrum changes to the absorptionlike one.
The numerical solution for polarization for two-level atom in polyharmonic field has been made. The analytical solution for partial case of symmetrical position of carrier frequency relative to transition frequency is possible. The results showed that the nonlinear features in polarization spectrum take place even for small amplitudes of comb-components for small frequency distance between them. It means that it is necessary to take into account nonlinear effects for interpretation of spectra in comb spectroscopy.