All-Optical Photoluminescence Response of Nitrogen-Vacancy Ensembles in Diamond at Low Magnetic Fields

TL;DR

This paper investigates all-optical, microwave-free magnetometry using dense NV ensembles in diamond at low magnetic fields (<2 mT). By correlating AO-PL contrast with near-degenerate NV spin and hyperfine transitions across orientations and validating with a two-NV dipolar-interaction model, the authors reveal coherent cross-relaxation mechanisms that shape AO-PL signals. They demonstrate CW-like DC magnetometry using AO-PL with sensitivities around 30 nT/√Hz and analyze how laser power and NV concentration govern the maximum AO-PL contrast, supported by rate-equation and density-matrix models. The findings suggest AO NV sensing can achieve high sensitivity with simpler hardware, offering opportunities for low-SWaP quantum sensing and extensions to other defect systems.

Abstract

All-optical (AO), microwave-free magnetometry using nitrogen-vacancy (NV) centers in diamond is attractive due to its broad sample compatibility and reduced experimental complexity. In this work, we investigate room-temperature AO photoluminescence (PL) at low magnetic fields (<2 mT) using diamonds with NV ensembles at ppm concentrations. Measured AO-PL contrast features as a function of applied magnetic field magnitude and direction are correlated with near-degenerate NV electronic spin and hyperfine transitions from different NV orientations within the diamond host. Reasonable agreement is found between low-field AO-PL measurements and model-based simulations of the effects of resonant dipolar interactions between NV centers. Maximum observed AO-PL contrast depends on both NV concentration and laser illumination intensity at 532 nm. These results imply different optimal conditions for low-field AO NV sensing compared to conventional optically detected magnetic resonance (ODMR) techniques, suggesting new research and application opportunities using AO measurements with lower system complexity, size, weight, and power.

Figures (19)

• Figure 1: (a) NV energy levels and couplings allow optical initialization of electronic spin states and emission of spin-state-dependent photoluminescence (PL). (b) AO-PL measurements utilize three sets of Helmholtz coils to control bias magnetic field magnitude and direction. NV centers in a single crystal diamond plate are optically excited by 532 nm laser light and emit PL ($\approx$ 637–800 nm), collected by a photodiode (not shown). A microwave antenna (not shown) enables comparison CW-ODMR measurements. Inset: dipolar interactions between different NV centers contribute to AO-PL contrast at low magnetic fields. (c) Illustration of avoided crossing from two interacting near-resonant NV electronic spins at low magnetic fields (<2 mT). Resonant NV-NV dipolar interactions at the avoided crossing increase the NV depolarization rate and reduce total PL emission.
• Figure 2: (a) Illustration of applied magnetic fields and four NV orientations along unit vectors $\hat{n}_\lambda$, $\hat{n}_\phi$, $\hat{n}_\chi$ and $\hat{n}_\kappa$. The on-axis magnetic field $B_{\parallel}$ is along the [111] crystallographic axis. The off-axis magnetic field $B_{\perp}$ is along the [$\bar{1}$10] crystallographic axis. $\theta$ is the polar angle from $B_{\parallel}$. (b) Experimentally determined AO-PL contrast as a function of applied magnetic fields using sample S1-14N with $\approx 3.8$ ppm NV concentration. Large AO-PL contrast around zero applied field, as well as line features at specific $\theta$ values are observed. (c) Simulated AO-PL contrast using a fixed dipolar interaction strength. (d) Expanded view of the upper right quadrant in Fig. \ref{['fig:concentration_spectrum']}(c), with labels at specific line features indicating the cross-relaxation between NVs of orientations along (i) $\hat{n}_\phi$, $\hat{n}_\chi$ and $\hat{n}_\kappa$ at $\theta = 0$°; (ii) $\hat{n}_\kappa$ at $\theta = 22.2$°; (iii) $\hat{n}_\lambda$ and $\hat{n}_\chi$; $\hat{n}_\phi$ and $\hat{n}_\kappa$ at $\theta = 39.3$°; (iv) $\hat{n}_\lambda$ and $\hat{n}_\kappa$ at $\theta = 58.5$°; (v) $\hat{n}_\lambda$ and $\hat{n}_\phi$ at $\theta = 90$°. NV hyperfine interactions contribute to parallel line structures within AO-PL contrast features.
• Figure 3: (a) Experimentally measured AO-PL contrast as a function of $B_{\parallel}$ and $B_{\perp}$ using $^{14}$N-enriched sample S1-14N (top) and $^{15}$N-enriched sample S2-15N (bottom) with the same NV concentration ($\approx$ 3.8 ppm). Horizontal dashed lines (orange for S1-14N and purple for S2-15N) indicate line-cut of data shown in Fig. \ref{['fig:14vs15']}(b) for $B_{\parallel}$ = 1.24 mT. (b) Experimentally measured AO-PL contrast for samples S1-14N and S2-15N (solid lines) and numerical simulations (dashed lines) at fixed $B_{\parallel} =$ 1.24 mT. Vertical offsets are applied to the simulation results for visual clarity. In each measurement as $B_{\perp}$ approaches 0 mT, there are overlapping, unresolved AO-PL contrast peaks from the increased number of near-degenerate spin transitions for all NV orientations. At $B_{\perp} \approx 0.5$ mT, the limited SNR in experimental measurements hinders the identification of cross-relaxation features predicted by numerical simulations. At $B_{\perp} \approx 1.05$ mT, there are five (three) AO-PL contrast peaks with separation $\Delta B_{14N} \approx 0.09$ mT ($\Delta B_{15N} \approx 0.13$ mT) and amplitude ratio of 1:2:3:2:1 (1:2:1) in the top (bottom) data and simulations, respectively, consistent with the effect of NV hyperfine interactions in the two samples.
• Figure 4: (a) Normalized AO-PL lock-in amplifier (LIA) measurements as a function of $B_{\perp}$ from $^{15}$N-enriched sample S2-15N at fixed $B_\parallel =$ 1.24 mT. Focus is on LIA features around 0.5 mT (purple) and 1 mT (orange). (b) AO-PL LIA signals with a smaller $B_\perp$ step size ($\approx$ 0.002 mT) from shaded areas in (a). Two weak features are observed in the shoulder of the dispersive signal with central zero crossing at about 0.53 mT (left). Near 1 mT, three dispersive features are measured with splitting $\Delta B_{15N} \approx 0.13$ mT (right). For both (left) and (right), vertical dashed lines indicate near-degeneracy of hyperfine transitions. (c) Summary of measurements of microwave-based CW-ODMR NV spin transition frequencies as a function of $B_{\perp}$, including different NV orientations and hyperfine splitting, for the same sample (S2-15N) and at fixed $B_\parallel =$ 1.24 mT. Between $B_{\perp} \approx$ 0.4 mT and 0.65 mT (left), NVs along orientation $\hat{n}_\kappa$ experience near-zero total applied magnetic field, leading to multiple avoided crossings between the hyperfine-split $\ket{m_s = +1 \leftrightarrow 0}$ and $\ket{m_s = -1 \leftrightarrow 0}$ spin transitions. Between $B_{\perp} \approx$ 0.8 mT and 1.3 mT (right), results are shown for all NV orientations, including only hyperfine-split $\ket{m_s = +1 \leftrightarrow 0}$ transitions for better clarity. (Consistent CW-ODMR results are found for $\ket{m_s = -1 \leftrightarrow 0}$ transitions.) Two groups of NV spin resonances are observed, each of which consists of two different NV orientations (along $\hat{n}_\lambda$ and $\hat{n}_\chi$; $\hat{n}_\phi$ and $\hat{n}_\kappa$). Within each spin resonance group, a single hyperfine resonance overlaps at both $B_{\perp} \approx$ 0.93 mT and 1.19 mT; whereas two hyperfine resonances overlap at $B_\perp \approx$ 1.05 mT. $B_\perp$ values for near-degenerate spin transition frequencies align well with those of zero crossings in the AO-PL LIA signals in (b), indicated by vertical dashed lines.
• Figure 5: AO-PL contrast at $B_{\parallel} = 1.24$ mT and $B_\perp = 1.05$ mT as a function of laser power and intensity for samples S3-14N ([NV] $\approx$ 3.8 ppm) and S4-14N ([NV] $\approx$ 2 ppm). The laser intensity is calculated by approximating a Gaussian excitation laser beam profile of radius $\approx$ 30 $\mu m$ (see Appendix \ref{['supp:exp']}). Markers indicate values determined from experimental measurements, with the standard deviation given by error bars; solid lines are from a rate-equation model with NV-concentration and spin-resonance-dependent relaxation rates between spin sublevels. For both samples, the contrast exhibits a maximum determined by the trade-off between optical pumping and spin relaxation. Sample S3-14N has higher overall AO-PL contrast, for all laser powers, because of its larger [NV] and hence stronger NV-NV dipolar interactions and cross-relaxation features.