Ground state cooling of nanomechanical resonator via parametric linear coupling

We present a ground state cooling scheme for a nanomechanical resonator linearly coupled with a LC oscillator. The linear coupling, when periodically modulated at red detuning, up-converts the low-frequency nanomechanical mode to the high-frequency LC oscillator mode and generates backaction force that can cool the resonator to its ground state in the resolved-sideband regime. We also study the effect of the quantum backaction noise on the cooling due to the counter rotating term in the linear coupling. The scheme can be compared with laser cooling for the atomic systems and can be realized in superconducting circuits.