Trapping conditions for a three-level atom interacting with cavity fields

The interaction between a single-mode cavity field and a string of three-level atoms of cascade type with equally spaced energy levels is investigated. The matrix elements of dipole transitions between adjacent levels are different. Trapping conditions for the flying time in the cavity as well as the explicit state of the field are found. The results are shown to be qualitatively different from the case of two-level systems. The properties of cavity fields are examined. In various limits, the state exhibits vacuum nutation as well as sub-Poissonian statistics and squeezing properties.