Fig. 2: Libration occupation number as a function of cavity detuning.

a, Heterodyne libration spectrum measured with the free-space backward detector (black), superposed with the cavity lineshape (blue dashed line). The detuning Δ is the difference between the tweezer frequency and the cavity resonance frequency. Highlighted in grey are the Stokes and anti-Stokes librational sidebands. For Δ ≈ Ω_α, with Ω_α/(2π) = 1.08 MHz being the librational frequency, the cavity enhances the anti-Stokes scattering, leading to resolved-sideband cooling. b, Stokes (left) and anti-Stokes (right) heterodyne spectra \({S}_{VV}^{{\rm{het}}}\) normalized to the shot-noise level S_sn with fitted Lorentzian lines for Δ increasing from top to bottom as indicated in the plot. δω_S and δω_aS denote the frequency differences from the Stokes and anti-Stokes peak centres, respectively. c, Occupation number n obtained from sideband thermometry as a function of Δ. It reaches a minimum of n = 0.5(3) at Δ/(2π) = 1.13 MHz. Occupation values are extracted from Lorentzian fits to the heterodyne spectra. Error bars correspond to one standard deviation of the fitted asymmetries around the calculated occupation numbers. The dashed line marks the n = 1 threshold. The shaded area corresponds to a theoretical estimation of n based on libration-cavity coupling, laser phase noise, radiation-torque shot noise and their uncertainties (Supplementary Information).