EFFECT OF A SQUEEZED VACUUM ON COHERENT POPULATION TRAPPING IN A 3-LEVEL-LAMBDA SYSTEM

Master equation methods are used to investigate the effects of a broad -band squeezed vacuum on a three-level atom of the lambda configuratio n. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed v acuum the atom is driven by two coherent laser fields each of which, d epending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for t he atomic density matrix elements have oscillatory coefficients, there by necessitating the use of Floquet methods. For the case of equal las er frequencies, which are also equal to the carrier frequency of the s queezed vacuum, the coefficients of the Bloch equations become time in dependent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the u sual coherent population trapping effect at two-photon resonance is ob tained, with the upper state population being zero. An unsqueezed ther mal field partially destroys the trapping effect as the upper state po pulation is no longer zero at two-photon resonance. The squeezed vacuu m has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which oc curs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of thi s coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of uneq ual laser frequencies, the coherence transfer process in combination w ith the squeezed vacuum can restore to some extent the population trap ping. We show that other features that do not occur for two-level atom s, such as stationary population inversions between pairs of the atomi c levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fi elds the population in the upper state depends on the relative phase o nly when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequen cy of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the d egree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.