Figure 4: Mechanical displacement noise.
From: Quantum electromechanics on silicon nitride nanomembranes
(a) Schematic showing the pump detuning and scattered microwave signals used to measure the mechanical resonator’s displacement noise. (b) Plot of the measured mechanical resonator bath phonon occupation (nb,m) and effective temperature (Tm) as a function of the fridge temperature (Tf). Each data point corresponds to the average inferred occupancy for blue detuned driving (Δr,d=−ωm) at low cooperativity (C<<1). Error bars corresponding to the s.d. in the inferred occupancy over several temperature sweeps. Calibration in units of occupancy is performed using a fit to equation (3) as described in the main text and Supplementary Notes 6–8. The grey dashed lines show the expected Bose–Einstein distribution 
assuming perfect thermalization to the fridge. (c) Plot of the dynamic backaction cooling of the mechanical resonator versus drive power (P0=1 mW) at three different fridge temperatures: Tf=235 mK (nf,m=1100; open circles), Tf=114 mK (nf,m=530; open squares) and Tf=26 mK (nf,m=120; open triangles). Data points showing the estimated average phonon occupancy of the fundamental in-plane flexural mode at ωm/2π≈4.48 MHz (nm) are shown as blue symbols, whereas data points for the estimated microwave cavity photon occupancy at ωr/2π=7.498 GHz (nr) are shown as orange symbols. The corresponding effective mode temperature, Tm, of the flexural mechanical mode is also shown on the right vertical axis. The solid line blue curves correspond to a model for the expected mechanical mode occupancy using a fit to the measured drive power relation for G and the microwave cavity parameters from coherent two-tone spectroscopy, the intrinsic mechanical damping from low power thermometry measurements and a fit to the power dependence of the microwave resonator occupancy. (d) Measured anti-Stokes noise displacement spectrum for several different drive powers at Tf=26 mK (blue data points). Fits to the measured spectra are shown as red solid lines (see Supplementary Note 6 for fit model). Extracted values for nm and nr are indicated and correspond to the results presented in c. Zoom-ins of the cavity noise and measured noise peaks are shown as insets.
