Probing the Dynamics of a Nuclear Spin Bath in Diamond through Time-Resolved Central Spin Magnetometry

Using fast electron spin resonance spectroscopy of a single nitrogen-vacancy defect in diamond, we demonstrate real-time readout of the Overhauser field produced by its nuclear spin environment under ambient conditions. These measurements enable narrowing the Overhauser field distribution by postselection, corresponding to a conditional preparation of the nuclear spin bath. Correlations of the Overhauser field fluctuations are quantitatively inferred by analyzing the Allan deviation over consecutive measurements. This method allows us to extract the dynamics of weakly coupled nuclear spins of the reservoir.

Figure 1

Hyperfine structure of a single NV defect interacting with nearby ${}^{13}\mathrm{C}$ nuclear spins. Hyperfine sublevels linked to the intrinsic ${}^{14}\mathrm{N}$ nuclear spin of the NV defect are not shown. The right panel shows a typical spectrum of the ESR transition between the $m_s=0$ [$|0_e⟩$] and $m_s=-1$ [$|-1_e⟩$] electron spin sublevels.

Figure 2

(a) Intensity plots of consecutive ESR spectra recorded at different magnetic fields. Pulsed-ESR spectroscopy is performed with a MW $\pi$-pulse duration of $3\mu \mathrm{s}$. Markers show the ESR frequencies obtained by fitting each individual ESR spectrum with a Gaussian function. The error bars indicate the fit uncertainty with a 95% confidence interval. (b) Time evolution of the instantaneous ESR frequency over 630 consecutive individual spectra recorded at different magnetic fields (total acquisition time $\sim 300\mathrm{s}$). The right panels show the corresponding histograms. (c) Top panel: Averaged sum of individual ESR spectra recorded at $B=4000\mathrm{G}$. The inhomogeneous linewidth is $403\pm 6\mathrm{kHz}$. Lower panels: Selected individual ESR spectra recorded at $B=4000\mathrm{G}$. Statistical analysis over the set of 630 individual spectra leads to an ESR linewidth of $280\pm 70\mathrm{kHz}$, limited by the $\pi$-pulse duration used for pulsed-ESR spectroscopy.

Figure 3

(a) Distribution of consecutive ESR frequencies at three different magnetic fields. (b) Post-selected ESR spectra obtained by summing experimental runs $i+1$ conditioned by $f(i)>0$ (upper panels) or $f(i)<0$ (lower panels). The black dashed lines correspond to ESR spectra averaged over all individual runs. Solid lines are fits with Gaussian functions. At $B=4000\mathrm{G}$, the linewidth of the postselected ESR spectrum is reduced to $303\pm 5\mathrm{kHz}$. (c) Allan deviation ${\sigma }_{\mathrm{A}}(k)$ inferred from the set of ESR frequencies $\{f(i)\}$ at different magnetic fields. Solid lines are data fitting with Eq. (3) leading to ${\mathcal{A}}^{(1)}=210\pm 7\mathrm{kHz}$. Inset: Relaxation time $T_R$ inferred from data fitting as a function of the magnetic field. The solid line is a quadratic fit as predicted by Eq. (1).

Figure 4

(a) Intensity plots of consecutive ESR spectra recorded for NV2 with a MW $\pi$-pulse duration of $4\mu \mathrm{s}$. (b) Allan deviations inferred from a set of 300 consecutive ESR spectra at different magnetic fields. Solid lines are data fitting with Eq. (3), as explained in the main text. At high fields, we obtain $T_R=2.6\pm 0.2\mathrm{s}$ and $\sqrt{[{\mathcal{A}}_{\mathrm{zz}}^{(2)}{]}^2+[{\mathcal{A}}_{\mathrm{zz}}^{(3)}{]}^2}=45\pm 2\mathrm{kHz}$. The latter value is in decent agreement with the one inferred from the dynamical decoupling signal (see Table 1). (c) Dynamical-decoupling signal obtained by implementing a 32-pulse sequence (see inset) with a magnetic field $B=500\mathrm{G}$. The solid line is data fitting using the procedure described in Ref. [29]. More details can be found in the Supplemental Material [25].