Phase-dependent properties of absorption and dispersion in a three-level closed-loop lambda atomic system

We examine the absorption and dispersion properties of a weak probe field in a three-level lambda system closed by a microwave field. We find that, due to quantum interference in this closed-loop atomic system, the absorption and dispersion properties of a weak probe field depend on the relative phase of the applied fields. A large inversionless gain and a large index of refraction with zero absorption can be obtained by tuning the relative phase into proper values. In the case of three-photon off-resonance, the probe gain (absorption) exhibits periodically oscillatory behavior versus time.