Quantum statistical theory of optical-resonance phenomena in fluctuating laser fields

A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\alpha$ above the threshold and for $\alpha \gg {\gamma }_c$; however, now the peak heights (widths) are in the ratio $3x$ ($\frac{2}{3x}$), $x=\frac{[{\gamma }_c+\frac{(T_1^{-1\mathrm{}}+T_2^{-1\mathrm{}})}{3}]}{[2\mathrm{}{\gamma }_c+T_2^{-1\mathrm{}}]}$, where ${\gamma }_c^{-1\mathrm{}}$ is the correlation time for laser phase fluctuations. For ${\gamma }_c\gg \alpha$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.