Aspects of the competition between atom-field and field-environment   couplings under the influence of an external source in dispersive   Jaynes-Cummings model
  We give a fully description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom-field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any initial state and we show that atom-field steady state is at most classically correlated. For an initial state chosen, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. Moreover, we show that the degree of entanglement of the atom-field state, for the particular initial state chosen, can be completely quantified by concurrence. Analytical expression for time evolution of the concurrence is given. 
J. G. Peixoto de Faria, M. C. Nemes