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

We study cooling and squeezing the fluctuations of a nanomechanical beam using quantum feedback control. In our model, the nanomechanical beam is coupled to a transmission line resonator via a superconducting quantum interference device. The leakage of the electromagnetic field from the transmission line resonator is measured using homodyne detection. This measured signal is then used to design a quantum feedback control signal to drive the electromagnetic field in the transmission line resonator. Although the control is imposed on the transmission line resonator, this quantum feedback control signal indirectly affects the thermal motion of the nanomechanical beam via the inductive beam-resonator coupling, making it possible to cool and squeeze the fluctuations of the beam, allowing it to approach the standard quantum limit.