Magnetic Resonance Detection of Individual Proton Spins Using Quantum Reporters

We demonstrate a method of magnetic resonance imaging with single nuclear-spin sensitivity under ambient conditions. Our method employs isolated electronic-spin quantum bits (qubits) as magnetic resonance “reporters” on the surface of high purity diamond. These spin qubits are localized with nanometer-scale uncertainty, and their quantum state is coherently manipulated and measured optically via a proximal nitrogen-vacancy color center located a few nanometers below the diamond surface. This system is then used for sensing, coherent coupling, and imaging of individual proton spins on the diamond surface with angstrom resolution. Our approach may enable direct structural imaging of complex molecules that cannot be accessed from bulk studies. It realizes a new platform for probing novel materials, monitoring chemical reactions, and manipulation of complex systems on surfaces at a quantum level.

Figure 1

Characterization of surface reporter spins using a shallow NV center. (a) Schematic of a network of reporter electron spins $s$ on the surface of a diamond crystal, that can be used to detect and localize surface proton spins $p$. (b) DEER pulse sequence. (c) Measured DEER signal as a function of reporter spin frequency (${\omega }_s/2\pi$) for fixed $t_{\mathrm{NV}}$. (d) Measured and calculated Zeeman shifts of NV (blue) and reporter (red) spin states. (e) Results of DEER experiment with varying echo delay time $t_{\mathrm{NV}}$. Green squares and line: NV center spin echo decay data and fit. Red circles: DEER measurements. Blue triangles: DEER measurements after oxidizing acid treatment. Red and blue lines are fits using a model with positions of reporter spins on the diamond surface as fitting parameters. In this and subsequent figures, spin state populations are scaled to range between $-1$ and $+1$. (f) Probability density map for surface reporter spins near NV A [depth $(3.3\pm 0.2)\mathrm{nm}$], marked by the red dot. Arrows mark diamond crystallographic axes; NV center is aligned along (111).

Figure 2

(a) Coherent control of reporter spins. Rabi oscillations between spin states with a variable-width pulse (red points) with an exponentially damped fit (blue line). Inset: rf pulse sequence. (b) Population relaxation dynamics of the reporter spins (red points) with an exponential-decay fit (blue line). Inset: rf pulse sequence.

Figure 3

Detection of the magnetic field created by protons, using the surface electron reporter spins. (a) Measurement with NV A of the reporter spin-echo modulation at $B=383\mathrm{G}$ (red points), fit with a model for echo modulation of a reporter spin coupled to a nuclear spin bath [19] (fit shown by blue line, reduced chi-squared value is 1.2). The error bars on this and subsequent plots show standard deviations of the data points obtained from averaging approximately 5 million repetitions of the pulse sequence, and are consistent with photon shot noise. Inset: reporter echo pulse sequence. (b) Measured values for ${\omega }_n$ at 5 different settings of the applied static magnetic field (blue points), consistent with the proton gyromagnetic ratio of $2\pi \times 4.26\mathrm{kHz}/\mathrm{G}$ (blue line). The red points mark the ${\omega }_n$, ${\omega }^{-}$, and ${\omega }^{+}$ oscillation frequencies; see text.

Figure 4

Coherent dynamics between individual surface electron and proton spins. (a) Reporter spin-echo modulation for NV A at $B=619\mathrm{G}$ (red points), and fit using a model with the reporter qubit, proximal to the NV center, coupled to one proton spin (blue line). (b) Reporter spin-echo modulation with NV B at $B=665\mathrm{G}$ (red points). The best-fit (blue line, reduced chi-squared value of 1.1) corresponds to a model with the reporter qubit, proximal to the NV center, coupled to two proton spins. (c) Schematic illustrating hyperfine coupling between the reporter electron spin $s$ and the proton spins (gold arrows). The weakly coupled protons far from the reporter spin precess in the applied magnetic field $B$ at the Larmor frequency. The proximal proton spin $p$ experiences the vector sum of $B$ and the effective hyperfine fields $\pm a/2{\gamma }_n$ and $\pm b/2{\gamma }_n$, whose signs depend on the reporter spin state. (d) Energy level diagram for the coupled system of the reporter spin and proximal proton spin. (e) Localization of the two proximal proton spins ($p_1$ and $p_2$) relative to the reporter spin $s$, which is most strongly coupled to NV B. The color scale shows the probability density for each proton location, extracted from a fit to the data shown in (b) [19].