Sympathetic cooling of a radio-frequency LC circuit to its ground state in an optoelectromechanical system

We present a complete theory for laser cooling of a macroscopic radio-frequency LC electrical circuit by means of an optoelectromechanical system, consisting of an optical cavity dispersively coupled to a nanomechanical oscillator, which is in turn capacitively coupled to the LC circuit of interest. The driven optical cavity cools the mechanical resonator, which in turn sympathetically cools the LC circuit. We determine the optimal parameter regime where the LC resonator can be cooled down to its quantum ground state, which requires a large optomechanical cooperativity, and a larger electromechanical cooperativity. Moreover, comparable optomechanical and electromechanical coupling rates are preferable for reaching the quantum ground state.