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Considering the intrinsic nonlinearity in a nanomechanical resonator coupledto a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanicalQED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings modeldescribes the dynamics of this qubit-resonator system. Using quantum regressiontheorem and master equation approach, we have calculated the two-timecorrelation spectrum analytically. In the weak driving limit, these analyticalresults clarify the influence of the driving strength and nonlinearityparameter on the correlation spectrum. Also, numerical calculations confirmthese analytical results.

Vacuum Rabi Splitting in Nanomechanical QED System with Nonlinear Resonator