Optical coherent transients: Generalized two-level solutions

Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole ($T_2$) and population ($T_1$) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\gamma }_1\ne {\gamma }_2$) and the lifetime $T_1$ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\gamma }_1\ne {\gamma }_2$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.