Microwave-free vector magnetometry and crystal orientation determination with nitrogen-vacancy centers using Bayesian inference

Commun. Phys. (2026) · DOI: 10.1038/s42005-026-02736-y · arXiv: 2512.13835

License: CC BY 4.0.

Abstract

Nitrogen-vacancy (NV) centers in diamond provide a solid-state platform for quantum sensing. While optically detected magnetic resonance techniques offer high sensitivity, their reliance on microwaves introduces heating and stray electromagnetic fields that can perturb nearby samples. Optical approaches based on cross-relaxation between differently oriented NV centers remove this constraint but have so far required stringent alignment of the external field with crystallographic axes, restricting their practicality. Here we introduce a general framework for microwave-free vector magnetometry at near-zero field that leverages Bayesian inference to extract both the magnetic field vector and the NV orientation directly from photoluminescence maps. An analytical model of cross-relaxation resonances enables efficient inference under arbitrary field and orientation configurations, while naturally incorporating the discrete degeneracies of the NV symmetry. We experimentally demonstrate robust orientation determination and vector-field reconstruction, establishing a general route toward compact and alignment-free NV magnetometers for practical sensing applications.

Figures

14 panels with data across 4 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 2

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 3

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 4

• panel (a): Experimental photoluminescence map: normalised contrast (Arb.) against the axial bias field $B^{\mathrm{bias}}$ (mT) and the transverse field angle $\phi$ (radians), for a diamond crystal with a randomly selected orientation. data.csv
• panel (b): Simulated photoluminescence map with the inferred parameters: normalised contrast (Arb.) against the axial bias field $B^{\mathrm{bias}}$ (mT) and the transverse field angle $\phi$ (radians), on the axes of panel (a). data.csv
• panel (c-1): Marginal posterior $P(\alpha,\beta\,|\,y)$ for the diamond orientation against $\alpha$ (rad) and $\beta$ (rad), around the MAP 1 solution: the upper left plot of panel (c). The peak is bright here and dark in the print. data.csv
• panel (c-2): Marginal posterior $P(\alpha,\beta\,|\,y)$ for the diamond orientation against $\alpha$ (rad) and $\beta$ (rad), around the MAP 2 solution: the upper right plot of panel (c). The peak is bright here and dark in the print. data.csv
• panel (c-3): Marginal posterior $P(\zeta\,|\,y)$ against $\zeta$ (rad) on a broken axis, as printed, with one peak for each of the two orientations of the upper plots: the bottom plot of panel (c). The peak labels #1 and #2 of the print are not drawn. data.csv

Fig. 5

• panel (a): Simulated photoluminescence map, PL (a.u.), against the bias field $B^{\mathrm{bias}}$ (mT) and the rotation angle $\phi$ (rad), with the laboratory $z$-axis, around which the sample is rotated, along the [100] crystal axis. data.csv
• panel (b): Simulated photoluminescence map, PL (a.u.), against the bias field $B^{\mathrm{bias}}$ (mT) and the rotation angle $\phi$ (rad), with the laboratory $z$-axis, around which the sample is rotated, along the [110] crystal axis. data.csv
• panel (c): Simulated photoluminescence map, PL (a.u.), against the bias field $B^{\mathrm{bias}}$ (mT) and the rotation angle $\phi$ (rad), with the laboratory $z$-axis, around which the sample is rotated, along the [111] crystal axis. data.csv
• panel (d): Simulated photoluminescence map, PL (a.u.), against the bias field $B^{\mathrm{bias}}$ (mT) and the rotation angle $\phi$ (rad), with the laboratory $z$-axis, around which the sample is rotated, along [123], a non-symmetric direction. data.csv

Fig. 6

• panel (a): Measured photoluminescence map: normalised contrast (Arb.) against the bias field $B^{\mathrm{bias}}$ (mT) and the rotation angle $\phi$ (radians), for a new magnetic-field configuration, with the diamond kept in the orientation found in Fig. 4. data.csv
• panel (b-1): Marginal posterior $P(b_z\,|\,y)$ against the field parameter $b_z$ (mT), the top plot of panel (b). It is shown over the peak region, the range of the printed inset, rather than the full printed axis. data.csv
• panel (b-2): Marginal posterior $P(b_\perp\,|\,y)$ against the field parameter $b_\perp$ (mT), the middle plot of panel (b). It is shown over the peak region, the range of the printed inset, rather than the full printed axis. data.csv
• panel (b-3): Marginal posterior $P(\varphi_0\,|\,y)$ against the field parameter $\varphi_0$ (rad), the bottom plot of panel (b). It is shown over the peak region, the range of the printed inset, rather than the full printed axis. data.csv

Fig. 7

• panel (b): Uncertainty $\Delta b_\perp$ ($\mu$T) of the inferred transverse field component against the number of data traces $N$, log-log. Markers are the mean posterior width over 1000 repetitions for each $N$, with the standard deviation across them drawn as a band where the print has error bars; the dotted line is the $\sim 1/\sqrt{N}$ scaling. data.csv

Cite

Hilario Espinós, Omkar Dhungel, Arne Wickenbrock, Dmitry Budker, Ricardo Puebla, Erik Torrontegui. Microwave-free vector magnetometry and crystal orientation determination with nitrogen-vacancy centers using Bayesian inference. Commun. Phys. (2026). https://doi.org/10.1038/s42005-026-02736-y

When you use hosted data, cite the original paper and give the panel's URL so a reader can find the exact values you used.

All papers · About · Statistics · Submit data · API