Extended Data Fig. 5: Data analysis.
From: Spin squeezing in an ensemble of nitrogen–vacancy centres in diamond
(a) Sample decay curves ⟨Sx(tr)⟩ comparing experimental and numerical data. Here, shelving has been used to prepare the initial state which is then squeezed for a time tg = 1.6μs. (b) The same data plotted in (a) after shifting each curve by to(tg, θ). (c) Comparison of the offset time calculated using the OAT model (purple) with direct numerical extraction of the offset time for these data (blue). (d, e) Comparison between the fitted decay timescales for experimental (d) and numerical (e) data. Here we also show the change in extracted timescale if the upper bound on the fitting window \({t}_{\max }\) is adjusted between 12 and 16 μs. (f, g) We plot the extracted T2 decay timescale for the numerical data (f) in the full parameter space {tg, θ}. Maximum and minimum T2 are indicated with the dashed blue and red lines, respectively. The same plot after mapping T2 to Var(Sθ) is shown in (g). (h) Red and blue curves show the maximum and minimum variances Var(Sθ) as a function of tg, corresponding to the dashed lines in (g). (i) Final mapping obtained by matching the timescale data plotted in (f) to the variance data plotted in (g). We observe that the dictionaries at different squeezing generation times tg (solid to transparent green) overlap, as expected. (j) Experimentally measured decay timescale, T2, as a function of preparation time tg and probing angle θ for the shelving method. For tg = 0, the measured decay timescale is independent of θ. As the NV ensemble evolves under the XXZ Hamiltonian, for a large range of global rotation angles, the decay timescale becomes longer; we note that such behavior is not expected for any external noise sources, but is naturally expected for spin squeezing dynamics.
