Theoretical Studies Of The Nonlinearity In Nanomechanical QED Effects

In nanomechanical QED system, consisting of a superconducting qubit and a nanomechanical resonator with intrinsic nonlinearity, we study the Rabi oscillation effect and vacuum Rabi splitting effect, the two typical quantum optical phenomena.In the study of the Rabi oscillation effect, using a nonlinear Jaynes-Cummings model,we describe the dynamical behavior of quantum system. Using microscopic master equation approach, we solve time evolution of the density operator. By calculating the probability of excited state of the superconducting qubit, we study the influence of the nonlinearity on Rabi oscillation in this nanomechanical QED system. In the study of the vacuum Rabi splitting effect, a driven nonlinear Jaynes-Cummings model is used to describe the dynamics of the quantum system. Using master equation and quantum regression theorem, we calculate the two-time correlation spectrum. In the weak driving limit, these analytically calculations clarify the influence of the nonlinearity parameter on the vacuum Rabi splitting. Also, we apply quantum optics toolbox(QuTip) programmed by Python to obtain the corresponding numerical simulations which confirm these analytical calculations.