Fig. 4: Feedback cooling and sensitivity.

a, Mean phonon occupation of the motion 〈nq〉 along x (blue triangles) and y (purple circles) for increasing feedback gains \({k}_{\rm{q}}^{\rm,d}\), extracted from the in-loop PSDs. The data points and error bars are the mean and s.d. of ten independent temperature measurements. The solid lines are fits to equation (4) with \({T}_{\rm{q}}^{{{\,{\rm{eff}}}}}\) given by equation (3) where \({{{\varGamma }}}_{\rm{q}}^{{{\,{\rm{fb}}}}}\) is the only free parameter. Other parameters are extracted from the in-loop PSDs. The shaded regions correspond to the uncertainty of the extracted parameters (Supplementary Information, section VI). b, PSD of the y motion for three different values of the feedback gain. The solid lines are fits to equation (2) (see text for details). c, PSDs of the force and acceleration sensitivities for the same three feedback gains as in b. The solid line is the minimum force and acceleration sensitivity from equations (5) and (6).