Simultaneous cooling and synchronization of the mechanical and the radio-frequency resonators via voltage modulation

We explore the ground state cooling and quantum synchronization of the mechanical and low-frequency inductor-capacitor (LC) resonators in a hybrid three-mode optoelectromechanical system, in which the mechanical resonator is optically and capacitively coupled to the optical cavity and the LC circuit, respectively. We find that when the bias voltage modulation switch is incorporated into the direct current (DC) bias voltage, ground state cooling and quantum synchronization can be simultaneously achieved regardless of whether the mechanical resonator and the low-frequency LC resonator have the identical frequency. Furthermore, we elucidate the relationship between quantum synchronization and ground state cooling of the two resonators, that is, the simultaneous ground state cooling of the resonators must be accompanied by quantum synchronization. Our work may open up an alternative approach to the simultaneous ground state cooling and quantum synchronization of multiple resonators, which has fewer parametric limitations.