Fig. 4: Free induction decay.

a, Collection of 600 Ramsey oscillations as a function of τ_wait, the free evolution time between two π_x/2 pulses, at θ_zx = 118^∘. The applied microwave frequency is detuned by ~700 kHz from the Larmor frequency. Each Ramsey oscillation is measured in ∼5.5 s. The locations of the representative traces shown in b are indicated by a diamond and a dot. b, Selected averages of Ramsey oscillations taken over different measurement times: t_meas = 5.5 s corresponding to a single trace (diamonds); t_meas = 27.5 s, corresponding to five consecutive traces (circles); t_meas ≈ 1 h, corresponding to the full set of 600 traces (squares). The solid lines are fits to Gaussian decaying oscillations. Note that the decay time \({T}_{2}^{* }\) depends on the chosen subset of consecutive traces (except for t_meas ≈ 1 h), which is a signature of non-ergodicity³⁶ at small t_meas (Supplementary Information, section 4). Hence we observe a distribution of \({T}_{2}^{* }\) values with mean \({\overline{T}}_{2}^{* }\). c, Mean \({\overline{T}}_{2}^{* }\) for different t_meas (same symbols as in b) as a function of the magnetic field angle θ_zx. The solid lines are guides to the eye. The dashed black line is the calculated dephasing time due to hyperfine interactions (Supplementary Information, section 5).