Effectively irreversible fringe contrast attenuation induced by one   degree of freedom
  The attenuation of fringe contrast in a Ramsey interferometer induced by the atom-field interaction is analyzed. We show that short-time power series expansion is not the proper tool to find the relevant time scale for such process. Analytical expressions to quantify the relevant time scale for the fringe contrast decay and to characterize the long-term effectiveness of this process are proposed. For Pegg-Barnett phase state initial conditions, these expressions suggest that: the increase of the energy of the field leads to slower vanishing of fringe contrast; the increase of the field photon number variance leads to more effective attenuation in the final regime. Numerical simulations with coherent and thermal initial states are in qualitative agreement with such results. 
A. R. Bosco de Magalh\~aes, and Ad\'elcio C. Oliveira