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Physics Letters A

On the time dependence of a degenerate two-level system interacting with a pulse of radiation

Gerald F. Thomas, William J. Meath

Published Apr 1, 1979• 9 citations
Publisher
DOI
10.1016/0375-9601(79)90343-8

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The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, Ip{I}_{\mathrm{p}}Ip​ and Iup{I}_{\mathrm{up}}Iup​, and the time-dependent degree of polarization P(t)P(t)P(t) are calculated. A method is based upon the Feynman-diagram technique which is extended to enable the calculation of the reduced-density matrix element. It is found that, for the step excitation, P(t)P(t)P(t) does not show a simple exponential decay. Especially in the off-resonance case, P(t)P(t)P(t) shows oscillatory behavior. In the case of pulse excitation, Iup{I}_{\mathrm{up}}Iup​ takes its maximum value after the excitation pulse has been turned off, and in the long-time limit it decays with the radiative-damping rate. In contrast to Iup{I}_{\mathrm{up}}Iup​, Ip{I}_{\mathrm{p}}Ip​ quickly responds to the excitation pulse and shows rapid exponential decay with the transverse-relaxation rate. It is also found that, contrary to the nondegenerate case, the total intensity of the secondary radiation does not exhibit simple exponential decay with the radiative-damping rate.
Mathematical modeling of the population dynamics is performed for states of a three-level system (atom) with a V-type configuration transforming a light pulse. It is assumed that the excited eigenstates of the atom are degenerate and coupled by coherent interaction, one of the states being radiating (radiative), while the other state is nonradiating (“dark”). The population dynamics of atomic states is described on the basis of numerical solutions of equations for the matrix elements of the density operator. The dependence of the efficiency of population of the atomic dark state from the values of the parameters of an irradiation pulse and from the ratio of the period of population oscillations of excited atomic states (caused by their coherent interaction) to the lifetime of the atomic radiating state is determined. Typical examples of the time dependence of the population of states of the atom considered are presented for the cases of irradiation by a short (as compared to the lifetime of the radiating state) sinusoidal light pulse and by a long rectangular light pulse with the resonance carrier frequency.