Effects of long-lived incoherences on coherent population trapping

Abstract

The effects of the non-Markov character of several types of relaxation on population trapping are examined. Different types of relaxation can arise as a result of (i) intermediate-state interactions and (ii) the non-Lorentzian character of the lineshapes of the pump and probe beams used for the study of the trapping. In each case the dynamical equations for the appropriately defined elements of the density matrix will have multiplicative colour noise, for which the correlation time τ_c, need not be short. A very interesting regime of physical behavior is obtained if the correlation time and of the Rabi frequencies, G_i, of the transitions are such that G_iτ ⋍1. The relevant mathematical equations for the two mechanisms of relaxation, (i) and (ii), are related using methods based on Fokker-Planck equations and matrix continued fractions; the authors calculate physical quantities such as excited-state populations and coherences for a range of parameters including detunings, correlation times and pump and probe intensities. Under conditions of population trapping, Raman signals have the same form as Fano profiles.