  An open quantum bipartite system consisting of two independent two-level
atoms interacting non-linearly with a two-mode electromagnetic cavity field is
investigated by proposing a suitable non-Hermitian generalization of
Hamiltonian. The mathematical procedure of obtaining the corresponding wave
function of the system is clearly given. Panchartnam phase is studied to give a
precise information about the required initial system state, which is related
to artificial phase jumps, to control the Degree of Entanglement (DEM) and get
the highest Concurrence. We discuss the effect of time-variation coupling, and
dissipation of both atoms and cavity. The effect of the time-variation function
appears as frequency modulation (FM) effect in the radio waves. Concurrence
rapidly reaches the disentangled state (death of entanglement) by increasing
the effect of field decay. On the contrary, the atomic decay has no effect.
