  In nanomechanical QED system, consisting of a charge qubit and a nonlinear
nanomechanical resonator, we study the temporal behavior of Rabi oscillation in
the nonlinear Jaynes-Cummings model. Using microscopic master equation
approach, we solve time evolution of the density operator describing this
model. Also, the probability of excited state of charge qubit is calculated.
These analytic calculations show how nonlinearity parameter and decay rates of
two different excited states of the qubit-resonator system affect
time-oscillating and decaying of Rabi oscillation.
