Collisional Redistribution from a Two-Level Atom and Resonance Fluorescence from a Three-Level Atom Interacting with a Monochromatic and Broadband Laser.

Two calculations on the spontaneous emission spectrum of a model atom are presented. The first calculation concerns a two-level atom interacting with a broadband laser as the atom undergoes collisions. The variable bandwidth of the laser is achieved using the phase diffusion model. While the collisions are modeled by assuming a randomly fluctuating energy separation between the atomic levels. The atom-field system is described in a fully quantized theory by employing the Heisenberg equations of motion for the atomic transition operators and the field operators. The equations of motion are also found for the two-time correlation functions of atomic operators. The operator equations are then averaged over the phase diffusion of the laser and the random collisions. The emission spectrum is then found by taking the Fourier transform of the correlation function between the atomic raising and lowering operators. From the Fourier transform analytic expressions for the spectrum are derived for both the low and high intensity laser field limit. The effects of laser detuning, collisions rates, and laser bandwidth on the emission spectrum are examined in detail. The second calculation involves the emission spectrum from a three-level atom interacting with a monochromatic and broadband laser. As in the two-level atom calculation, equations of motion are found for the atomic transition operators and field operators. The equations are averaged over the laser phase diffusion and the Fourier transform of the appropriate atomic correlation function is taken. The expressions for the spectrum is evaluated numerically and graphs are plotted for various values of laser field strengths, detunings, and laser bandwidths. The positions of the peaks and the heights, widths, and line intensities of the various spectral components are explained in terms of rate equation techniques developed by Cohen-Tannoudji and Renaud.