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arXiv:1208.4082 · Journal of Physics B Atomic Molecular and Optical Physics

Multiphoton population dynamics in a three-level lambda system and the related light-scattering spectrum

Michał Berent, R. Parzyński

Published Apr 27, 2011• 1 citation
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Abstract

We generalize our analytic approach (Berent, M. and Parzyński, R. (2009): Phys. Rev. A (80) 033834) to include the effect of strong depopulation of the initial state when considering the multiphoton population transfer and scattering of low-frequency light by a 3-level system in the lambda-type configuration. We discuss the quality of the approximations made, i.e., the adiabatic and generalized rotating-wave approximations.

DOI
10.1088/0953-4075/44/10/105502

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We generalize our analytic approach (Berent, M. and Parzyński, R. (2009): Phys. Rev. A (80) 033834) to include the effect of strong depopulation of the initial state when considering the multiphoton population transfer and scattering of low-frequency light by a 3-level system in the lambda-type configuration. We discuss the quality of the approximations made, i.e., the adiabatic and generalized rotating-wave approximations.
We calculate analytically both coherent and incoherent parts of the total spectrum of light scattered by a three-level system in either lambda or ladder configurations. The spectrum is restricted to the cases of the incident light pulse weakly depopulating the initial level and of the carrier frequency much lower than the excitation frequency in the system. We give special attention to the spectra under the conditions of different multiphoton resonances in the system and emphasize the effects resulting from the presence of the third level. The analytic theory is shown to explain the numerically calculated spectra as far as the number of frequency components, their positions in the spectrum, relative intensities, and sensitivity to the pulse shape are concerned.
The resonance fluorescence spectrum of a Λ-system excited by two resonant light fields is calculated using a Markov analysis. Analytical formulas are derived in the strong-field limit within and beyond the rotating wave approximation. It is shown that the resonance fluorescence of the system does not vanish during coherent population trapping. Its spectrum consists of two multiplets which are similar to a triplet in the resonance fluorescence spectrum of a two-level atom and lie at the electronic transition frequencies, together with two triplets located at the frequencies of four-photon processes involving the optical excitation fields. The latter are fundamental in character and impose limits on the lower bound of the dephasing rate for the Raman resonance owing to the effect of radiative decay of the dipole transitions on the dynamics of the ground state. The effect of four-photon dephasing on the absorption spectrum of a Λ-system is analyzed and found to lead to a substantial reduction in the depth of a dip in the absorption spectrum which vanishes as the laser field strength is increased.
The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.