  Considering the intrinsic nonlinearity in a nanomechanical resonator coupled
to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical
QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model
describes the dynamics of this qubit-resonator system. Using quantum regression
theorem and master equation approach, we have calculated the two-time
correlation spectrum analytically. In the weak driving limit, these analytical
results clarify the influence of the driving strength and nonlinearity
parameter on the correlation spectrum. Also, numerical calculations confirm
these analytical results.
