COHERENT POPULATION TRAPPING AND ELECTROMAGNETICALLY INDUCED TRANSPARENCY IN MULTI-ZEEMAN-SUBLEVEL ATOMS

We present a general formalism for studying the interaction between la ser fields and degenerate-Zeeman-sublevel atoms correct up to the firs t order in the weak probe field. We derive from this theory the equati ons of motion for a h-type system involving S-1/2,S- F = 2 <----> P-1/ 2,P- F' = 1 <----> S-1/2,S- F = 1 transitions in Rb-87 atoms. These eq uations are used to numerically investigate the coherent population tr apping (CPT) schemes in the S-1/2,S- F = 2 <----> P-1/2,P- F' = 1 tran sition induced by a linearly polarized pumping field and the electroma gnetically induced transparency exhibited in the weak probe spectrum i n the S-1/2,S- F' = 1 <----> P (1/2,) F' = 1 transition. We discuss th e effects of the CPT on the probe spectrum with and without the Dopple r broadenings by comparing the probe spectrum derived from the real sy stem with that derived from an ideal Lambda-type system. We show that the atoms in the CPT states are shielded from interacting with the pro be field while those in the absorbent states make contributions to the weak probe by the Raman anti-Stokes process, and the effect of the re al system on the probe field becomes equivalent to the ideal Lambda sy stem only in the strong CPT parameter regime.