Creation of two-dimensional circular motion of charge qubit

Abstract: We suggest a nanoelectromechanical setup which generates a particular type of motion - the circular motion of mesoscopic superconducting grain, where motion is described by entangled nanomechanical coherent states. The setup is based on mesoscopic terminal utilizing the AC Josephson effect between the superconducting electrodes and the grain, operating in the regime of the Cooper pair box controlled by the gate voltage. The grain is placed on the free end of the suspended cantilever, performing controlled two-dimensional mechanical vibrations. Required functionality is achieved by operating two external parameters, bias voltage between the superconducting electrodes and voltage between gate electrodes, by which the nanomechanical coherent states are formed and organised in a pair of entangled cat-states in two perpendicular spatial directions which evolve in time in the way to provide a circular motion.