An analytical solution is obtained when the Kerr medium and Stark shift are considered
as nonlinear interaction terms to the system containing two-qubit and two-mode elec-
tromagnetic field from the parametric amplifier. Dynamics of the population inversion,
cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit
interaction, the Kerr medium and the Stark shift. The population inversion of a qubit
presents periodic revivals and collapses. The results show that the entanglement and
the population inversion as well as the inversion have the same stable intervals, that
is, the collapse intervals. It is found that the Kerr medium and the Stark shift may
lead to reduction of the periods and the amplitudes of the population inversion and
the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit
entanglement and the population inversion, due to the Kerr medium, may be increased
by increasing the Stark shift and vice versa.