Figure 3. Effective mechanical energy decay rates extracted from ring-down measurements.

Mechanical dissipation rate measured on device A with the ring-down technique as a function of the number n_p of pump photons in the cavity at V_g=0 V and V_g=3.002 V, where n_p is proportional to the microwave power P_in applied at the input of the cryostat (see Supplementary Note 3). Red and blue data points correspond to red and blue detuned pumping, respectively. The measurements are well described by (red and blue lines) using g₀/2π=9.7 Hz in a and g₀/2π=42.6 Hz in b. The inset in b shows a ring-down measurement for n_p=1.4·10⁶. We plot the normalized vibration amplitude as a function of time t. The resonator is driven with a capacitive driving force for t<t₀. At t₀ the drive is switched off and the vibration amplitude decays freely (t>t₀). We fit the data with an exponential decay (black line) using with a decay rate . The vibration amplitude in ring-down measurements is larger than that in undriven displacement spectra, so that the motion in ring-down measurements can be resolved with lower n_p.