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We study cooling and squeezing the fluctuations of a nanomechanical beamusing quantum feedback control. In our model, the nanomechanical beam iscoupled to a transmission line resonator via a superconducting quantuminterference device (SQUID). The leakage of the electromagnetic field from thetransmission line resonator is measured using homodyne detection. This measuredsignal is then used to design a quantum-feedback-control signal to drive theelectromagnetic field in the transmission line resonator. Although the controlis imposed on the transmission line resonator, this quantum-feedback-controlsignal indirectly affects the thermal motion of the nanomechanical beam via theinductive beam-resonator coupling, making it possible to cool and squeeze thefluctuations of the beam, allowing it to approach the standard quantum limit.

Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control