Coherent population trapping in the stochastic limit

A 2–level atom with degenerate ground state interacting with a quantum field is investigated. We show, that the field drives the state of the atom to a stationary state, which is non–unique, but depends on the initial state of the system through some conserved quantities. This non–uniqueness follows from the degeneracy of the ground state of the atom, and when the ground subspace is two–dimensional, the family of stationary states will depend on a one–dimensional parameter. Only one of the stationary states in this family is a pure state, and this state coincides with the known population trapped state (zero population in the excited level |N C). Another one stationary state corresponds to an equal weight mixture of the excited level |3 and of the coupled state |C.