Two-photon coherence and steady-state saturated and inverted populations in three-level systems

We study the correlation between level populations, absorption and two-photon coherence in closed ∧ and V-shaped three-level systems interacting with two lasers of arbitrary intensity. Whereas it is well known that maximum two-photon coherence leads to population trapping in ∧-shaped three-level systems interacting with two equally detuned lasers, we demonstrate that minimum two-photon coherence, under saturation conditions, can lead to equal populations in all the levels of a ∧- or V-shaped system when the lasers are symmetrically detuned. Moreover we show that steady-state population inversion between one of the upper levels of a V-shaped system and the ground state can occur when either the detunings are asymmetrical or the upper states decay at different rates. It is shown that this population inversion does not lead to stimulated emission into the lasing modes. These effects are also correlated with two-photon coherence and are explained physically by a cross three-photon scattering process involving two laser photons of different frequencies.