Transient polarization characteristics associated with resonant light scattering by a degenerate two-level system

The time dependence of the polarized and unpolarized parts of the secondary-radiation intensity, $I_{\mathrm{p}}$ and $I_{\mathrm{up}}$, and the time-dependent degree of polarization $P\left(t\right)\mathrm{}$ 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, $P\left(t\right)\mathrm{}$ does not show a simple exponential decay. Especially in the off-resonance case, $P\left(t\right)\mathrm{}$ shows oscillatory behavior. In the case of pulse excitation, $I_{\mathrm{up}}$ 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 $I_{\mathrm{up}}$, $I_{\mathrm{p}}$ 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.