Extended Data Figure 1: Effect of excitation-pulse bandwidth on the measurement of T₁.

a, The red and blue lines shown the computed pulse bandwidth (‘normalized response’) for a 5-μs π pulse and a 100-μs π pulse, respectively, incident on a cavity with κ/(2π) = 23 kHz (green dashes). To illustrate the averaging effect of the pulse bandwidth on T₁ measurements, the expected Purcell T₁ curve (black line) as a function of spin–cavity detuning is plotted on the right axis, with T₁(0) = 0.35 s and κ/(2π) = 23 kHz. b, T₁ measurements for two different π-pulse lengths (see insets), measured on resonance with resonator A. Spin polarization is measured with a Hahn echo sequence and A_Q is rescaled by its value for T ≫T₁ (‘A_Q(T = ∞)’). Symbols are data and solid lines are exponential fits. The 100-μs π pulse (blue) yields T₁ = 0.35 s, which is in agreement with the Purcell rate. The 5-μs π pulse (red) yields T₁ = 0.65 s, a factor of two greater than the accurate value.