Extended Data Fig. 2: Experimental frequency accuracy.

(a) Thermomechanical reference spectra. Before each experimental run, a set of thermomechanical spectra is taken, with modulations off, to determine the value of the mechanical resonance frequencies ω_j. A typical set is shown. Spectra are averaged over 50 runs and fitted by a Lorentzian function, with uncertainty (standard deviation) in the extracted ω_j’s (grey dashed lines) between σ_ω,fit/(2π) = 20 − 24 Hz, estimated from the fit residuals. (b) Frequency stability of the mechanical modes. Resonator frequencies ω_j are extracted from thermomechanical resonance spectra, measured repeatedly over a duration of 90s. Error bars denote the ± 2σ fit uncertainty interval estimated from residuals. Over time, fluctuations in ω_j are observed with standard deviation σ_ω,fluct/(2π) = 43 − 64 Hz, depending on the mode. Correlated fluctuations across the modes indicate a common origin, that we attribute to fluctuations in the optical spring effect. This is compatible with the observation that mechanical modes with higher index and lower optomechanical couplings g_0,j experience smaller frequency fluctuations.