Relaxation times and symmetries in the nonlinear optical properties of a two-level system

In this work we introduce a methodology for the determination of the longitudinal and transversal relaxation times in a two-level system using symmetry properties of the optical responses in the frequency space εΔ1,Δ2. Employing the density matrix formalism and a perturbative scheme for the incident field amplitudes in the Four-wave mixing spectroscopy, the nonlinear macroscopic polarization is determined. The collective effects of the thermal reservoir are modeled as a time dependent frequency, whose manifestation is the broadening of the upper level according to a prescribed random function.