Extended Data Fig. 7: Nuclear spin lifetime.

a, Nuclear spin N₁ lifetime measurement, which is realised by toggling the two ESR frequencies corresponding to \(| {\Uparrow \rangle}\) and \(| {\Downarrow} \rangle\) of N₁, followed by electron spin single-shot measurement. This procedure essentially constitutes a nuclear spin quantum non-demolition measurement. Each data point represents the electron spin-up fraction difference Δf_↑, comparing \(| {\Uparrow \rangle}\) and \(| {\Downarrow \rangle}\). Each spin-up fraction is averaged over 40 single-shot measurements and conducted over ~ 80 ms. The red dotted line displays the discrimination threshold for determining whether the nuclear is in the \(| {\Uparrow \rangle}\) or \(| {\Downarrow \rangle}\). b, The quantum jumps⁵⁸ are observed throughout the measurement, with the time resolution limited by the electron spin measurement speed. In the histogram of integrated signal versus Δf_↑, the two major peaks fitted by two Gaussian curves correspond to the two nuclear spin states. The resulting error rate for nuclear spin discrimination is drawn in c, giving an error rate less than 0.1% for both \(| {\Uparrow \rangle}\) and \(| {\Downarrow \rangle}\) states assertions, with a discrimination threshold around -0.2. d, The lifetimes for \(| {\Uparrow \rangle}\) and \(| {\Downarrow \rangle}\) of N₁ are measured over 6 hours, which is fitted using P(t) = Aexp(− t/T₁) + B, yielding \({T}_{| \Uparrow \rangle }^{\rm{N}_{1}} \sim 174\,\rm{s}\) and \({T}_{| \Downarrow \rangle }^{\rm{N}_{1}} \sim 300\,\rm{s}\). The lifetimes of nuclear spins N₂ and N₃ are characterised similarly, giving \({T}_{| \Uparrow \rangle }^{\rm{N}_{2}} \sim 100\,\rm{s}\) and \({T}_{| \Downarrow \rangle }^{\rm{N}_{2}} \sim 196\,\rm{s}\), \({T}_{| \Uparrow \rangle }^{\rm{N}_{3}} \sim 153\,\rm{s}\) and \({T}_{| \Downarrow \rangle }^{\rm{N}_{3}} \sim 144\,\rm{s}\), and the nuclear spin flips are mostly caused by the ionization process during electron spin readout⁸.

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