Microscale Sensing with Strongly Interacting NV Ensembles at High Fields

TL;DR

This work tackles the sensitivity bottleneck of microscale NV‑ensemble NMR at high fields by introducing SHIELD, a microwave dynamical decoupling scheme that continuously suppresses NV–NV dipole‑dipole interactions while preserving coupling to the NMR signal. By engineering detuned 2π rotations around carefully chosen axes to achieve a magic‑angle condition, SHIELD yields a symmetric, commuting DD term $H_{dd}^{\text{sym}}$ and a reduced signal amplitude through a factor $f_r$, enabling dense diamonds to reach higher SNR than conventional CPMG especially at NV densities above ~0.4 ppm. Numerical simulations up to small NV clusters show SHIELD delivering 5–7× sensitivity gains over CPMG at 3 ppm, with a broad detectable frequency window from tens of kHz to MHz, and robustness to strain, impurities, and MW phase noise. The approach is compatible with high‑field NMR and heterodyne sensing, potentially enabling high‑resolution microscale spectroscopy in realistic diamond substrates.

Abstract

Advances in sensing devices that utilize nitrogen-vacancy (NV) center ensembles in diamond are driving progress in microscale nuclear magnetic resonance spectroscopy. Utilizing quantum sensing techniques in the high-field regime significantly boosts sensitivity by increasing thermal polarization and improves spectral quality via enhanced energy shifts. Compatible with the latter, a straightforward manner to further raise sensor sensitivity is to increase NV concentration, although this intensifies detrimental dipole-dipole interactions among NVs. In this Letter, we present a method for detecting NMR signals in high-field scenarios while effectively suppressing dipole-dipole couplings in the NV ensemble. Thus, this approach enhances sensitivity by combining highly doped diamond substrates and elevated magnetic fields.

Figures (8)

• Figure 1: Illustration of the setup: A [111] cut diamond hosts a dense ensemble of NV centers, exhibiting strong dipole-dipole interactions. A target sample containing nuclear spins is placed on the diamond surface, with a strong magnetic field in the order of Teslas is applied along the $z$-axis. Nuclear spins rotate at moderate speed due to an RF field resulting into a slowly oscillating signal, $B(t)$, that encodes sample information. Simultaneously, NV centers are controlled using an MW driving.
• Figure 2: Scheme of the protocol. (a) At the top, continuous RF driving induces Rabi oscillations of the sample nuclei, which results in the NMR signal $B(t)$. At the bottom, the blue square represents the MW pattern of our sequence SHIELD, which simultaneously captures $B(t)$ while suppressing dipole-dipole interactions. SHIELD includes an initial and final pulse, and in between, $M$ repetitions of two $m$ blocks of rotations around the axes $A$, $\bar{A}$, $\bar{B}$, and $B$, interspersed by $\pi$-pulses along the x-axis. These pulses imprint the function $F(t)$ with periodicity $T$ on the effective operators $\sigma^C_j$. (b) Relevant direction and angles. In the XY plane, the axes $A$ and $B$ are rotated by angles $-\alpha$ and $\alpha$ from the $y$-axis about the $z$-axis, and both axes --$A$ and $B$-- form the magic angle with the $z$-axis. The bisector of $A$ and $B$ defines direction $C$. The grey box inset illustrates the effective dynamics of the NV spins: the initial pulse polarizes the NV centers along the $x$-axis (green dot), then the MW scheme slightly rotates the initial state around $C$, inducing changes in $\langle S^{C\perp} \rangle$, where $C^{\perp} =C \times x$. For readout, the accumulated spin polarization along $C^{\perp}$ is transferred to $z$-axis via the final pulse of angle $\beta$ along the $x$-direction.
• Figure 3: Numerical results. In every graph, the NV density in the $x$-axis corresponds to the concentration of NV centers aligned with the external magnetic field. This direction is the preferential alignment in [111] diamond cuts Lesik2014Michl2014Fukui2014Miyazaki2014Osterkamp2019. (a) Oscillation amplitude of $\bar{s}^z$ for different NV concentrations. Purple curve corresponds to the CPMG protocol, while red and blue curves to SHIELD using the $A\bar{A}\bar{B}B$ and $A\bar{A}\bar{A}A$ MW blocks, respectively. (b) Expected SNR considering $\sqrt{N}$ scaling of the noise. For CPMG sequence, at $0.4$ ppm is reached the best sensitivity, while SHIELD protocols exhibit an increasing tendency of SNR for sensible concentrations. (c) Maximum dipole-dipole coupling, i.e., $d_{ij}/(2\pi)$, at different NV concentrations. This is computed by averaging the maximum dipole-dipole interaction over thousands of distinct configurations, each constituted, on average, by four NVs.
• Figure S1: Illustration of the effective direction of the MW driving $\hat{\mu}$, due to the Rabi amplitude in direction $\hat{\phi}$ and the detuning along $z$. The resultant angle that $\mu$ forms with $z$ is $\theta$. The upper-right inset shows the direction $\hat{\mu^{\perp}}$.
• Figure S2: Illustration showing the pertinent directions and angles to follow the analytical derivation. On the left, the 3D scheme, where A (B) forms with x in the XY plane an angle $\phi_A$ ($\phi_B$), defining the directions $\hat{\phi_A}$ and $\hat{\phi_B}$. On the right, side cuts of the sphere showing the planes containing $z$ and the directions $\hat{\phi_\mu}$.