Coherent population trapping in open systems: A coupled/noncoupled-state analysis

Coherent population trapping (CPT) with losses towards off-resonant levels is analyzed on the basis of the coupled/noncoupled states. We derive that at a long interaction time the noncoupled state is depopulated at a rate that is decreasing for decreasing Raman detuning. This behavior produces a narrowing of the dark resonance with the interaction time. The asymptotic evolution of the atomic system is completely characterized by the effective width Gamma(XC) of the noncoupled state. The analytic expression for this width evidences a quadratic dependence on the Raman detuning. This dependence implies that the width of the dark resonance decreases asymptotically with the inverse of the square root of the interaction time. This narrowing law, independent of the interaction scheme, has a general validity for CPT in open systems. Our analysis points out the differences between CPT with losses and CPT in closed systems. [S1050-2947(99)08707-7].