  The problem of the relationship between entanglement and two-qubit systems in
which it is embedded is central to the quantum information theory. This paper
suggests that the concurrence hierarchy as an entanglement measure provides an
alternative view of how to think about this problem. We consider mixed states
of two qubits and obtain an exact solution of the time-dependent master
equation that describes the evolution of two two-level qubits (or atoms) within
a perfect cavity for the case of multiphoton transition. We consider the
situation for which the field may start from a binomial state. Employing this
solution, the significant features of the entanglement when a second qubit is
weakly coupled to the field and becomes entangled with the first qubit, is
investigated. We also describe the response of the atomic system as it varies
between the Rabi oscillations and the collapse-revival mode and investigate the
atomic inversion and the Q-function. We identify and numerically demonstrate
the region of parameters where significantly large entanglement can be
obtained. Most interestingly, it is shown that features of the entanglement is
influenced significantly when the multi-photon process is involved. Finally, we
obtain illustrative examples of some novel aspects of this system and show how
the off-resonant case can sensitize entanglement to the role of initial state
setting.
