Figure 1

(a) Schematic setup. We measure NV centers weakly coupled to ${}^{13}\mathrm{C}$ nuclear spins. A dc magnetic field is applied using a movable permanent magnet. (b) Pulsed spin manipulation and readout. (c) Central concept. Conditional evolution of the ${}^{13}\mathrm{C}$ on the Bloch sphere during NV spin manipulation for ${}^{13}\mathrm{C}$ spin initially in state $|\uparrow ⟩$, where $|\uparrow ⟩,|\downarrow {⟩}_{\mathrm{nuc}}$ are defined as the eigenstates of the ${}^{13}\mathrm{C}$ spin when the NV electron spin is in the state $m_s=1$. Upper (lower) panel shows ${}^{13}\mathrm{C}$ evolution with the NV spin is initially in state $|0⟩$ ($|1⟩$). Gray boxes show evolution during spin echo (single $\pi$ pulse). Additional $\pi$ pulses push the conditional nuclear spin evolution further apart, increasing its entanglement with the NV. For clarity a sequence with an odd number of $\pi$ pulses is shown; the result is qualitatively the same for the even numbered sequences used in this work, but is more difficult to visualize.Reuse & Permissions

Figure 2

Coherent interaction of an NV-Center with a single ${}^{13}\mathrm{C}$ detected using XY4-8. (a) The evolution time between $\pi$ pulses $t$ is swept with a fixed magnetic field of 15 G, data (black) and fit (red). The blue line is the calculated response without the individual ${}^{13}\mathrm{C}$. The inset shows the calculated response to Hahn echo, XY4-4, and XY4-8. (b) The fluorescence is plotted as a function of $t$ and magnetic field strength $B$, with magnetic field oriented along the NV $\widehat{z}$ axis ($\alpha =0$, as defined in the inset). The dashed line highlights the data shown in (a). (c) Fluorescence as a function of $t$ and magnetic field orientation $\alpha$, with $B=19\mathrm{G}$. The black line displays the extracted dip position in both (b) and (c).Reuse & Permissions

Figure 3

Detection of a distant ${}^{13}\mathrm{C}$ with a XY4-8 sequence. As in Fig. 2 the NV fluorescence is shown as a function of (a) magnetic field strength B with $\alpha =0.26$ rad, and (b) magnetic field orientation $\alpha$, with $B=80\mathrm{G}$. The dip from the single ${}^{13}\mathrm{C}$ is visible within a spin-bath revival centered at $2\times 2\pi /{\omega }_0$.Reuse & Permissions

Figure 4

Simultaneous detection of three ${}^{13}\mathrm{C}$ nuclei. (a) and (b) NV fluorescence is shown vs evolution time $t$ and magnetic field orientation $\alpha$ (data and fit), the applied field strength is 19 G. The fit assumes three ${}^{13}\mathrm{C}$ spins and yields robust and unique individual coupling strengths, while fits assuming fewer ${}^{13}\mathrm{C}$ spins could not reproduce the data. The NV response along the dashed line is shown in (c) black, red: data, fit. The traces in the inset display the calculated response of the NV interacting separately with each ${}^{13}\mathrm{C}$, and with the spin bath alone (black).Reuse & Permissions