  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 non-coupled population
trapped state (zero population in the excited level. Another one stationary
state corresponds to an equal weight mixture of the excited level and of the
coupled state.
