Rate equations for a three-level system

Time-dependent rate equations for the populations of a three-level molecular system are derived from the density matrix in the limit, in which the dephasing time is shorter than any relevant time scale, and the cross relaxation (dephasing) times are faster than the time scale characterizing changes in the envelope of the pumping field. These equations reduce to results obtained by other authors when non-linear two photon effects and power broadening are neglected.