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 a t a long interaction time the noncoupled state is depopulated at a rate tha t is decreasing for decreasing Raman detuning. This behavior produces a nar rowing of the dark resonance with the interaction time. The asymptotic evol ution of the atomic system is completely characterized by the effective wid th Gamma(XC) of the noncoupled state. The analytic expression for this widt h evidences a quadratic dependence on the Raman detuning. This dependence i mplies that the width of the dark resonance decreases asymptotically with t he inverse of the square root of the interaction time. This narrowing law, independent of the interaction scheme, has a general validity for CPT in op en systems. Our analysis points out the differences between CPT with losses and CPT in closed systems. [S1050-2947(99)08707-7].