Abstract
The dissipation of the field in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels was studied. The initial degenerate atomic state affects the field coherence loss. When the degenerate atom is initially in an equal probability superposition state, the field coherence loss is smallest. It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field. When the degeneracy was considered, the coherence properties of the field could be affected by the reservoir qualitatively, if a nonlinear two-photon process is involved. This is different from the dissipation of one-photon JCM with degenerate atomic levels.