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We considered a nanoelectromechanical system consisting of a movableCooper-pair box qubit which is subject to an electrostatic field, and coupledto the two bulk superconductors via tunneling processes. We suggest that qubitdynamics is related to the one of a quantum oscillator and demonstrate that abias voltage applied between superconductors generates states represented bythe entanglement of qubit states and coherent states of the oscillator ifcertain resonant conditions are fulfilled. It is shown that a structure of thisentanglement may be controlled by the bias voltage in a way that gives rise tothe entanglement incorporating so-called cat-states - the superposition ofcoherent states. We characterize the formation and development of such statesanalyzing the entropy of entanglement and corresponding Wigner function. Theexperimentally feasible detection of the effect by measuring the averagecurrent is also considered.

Entanglement between charge qubit states and coherent states of nanomechanical resonator generated by AC Josephson effect