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We present a complete theory for laser cooling of a macroscopicradio-frequency LC electrical circuit by means of an optoelectromechanicalsystem, consisting of an optical cavity dispersively coupled to ananomechanical oscillator, which is in turn capacitively coupled to the LCcircuit of interest. We determine the optimal parameter regime where the LCresonator can be cooled down to its quantum ground state, which requires alarge optomechanical cooperativity, and a larger electromechanicalcooperativity. Moreover, comparable optomechanical and electromechanicalcoupling rates are preferable for reaching the quantum ground state.

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