Two electromagnetic fields (the stronger called the pump and the weaker called the signal) are allowed to interact with a four-level double λ-type system with two pairs of closely spaced levels. The present four-level system could also be viewed as an example of a double resonant system. Under the Doppler-free condition and using a semiclassical formulation of atom–field interaction, we derive the optical Bloch equations involving the said four-level system coupled to two external fields. These coupled optical Bloch equations are unsolvable in closed analytical form. In order to obtain the absorptive lineshapes, we use the usual perturbation method for getting the approximate analytical solution to the coupled optical Bloch equations for the density matrix elements. Through the off-diagonal complex density matrix elements, the introduction of phase angles between the levels participating in dipole-allowed transitions is automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. For on-resonance pump conditions, we obtain the usual Rabi splitting. The effects of two-photon resonances are clearly shown for off-resonance pump conditions.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (
T2) and population (
T1) 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 (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime
T1 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 ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.