Photonic-integrated quantum sensor array for microscale magnetic localisation

Nat. Commun. 17, 6185 (2026) · DOI: 10.1038/s41467-026-73701-0

License: CC BY 4.0.

Abstract

Nitrogen-vacancy centres (NVs) are promising solid-state nanoscale quantum sensors for applications ranging from material science to biotechnology. Using multiple sensors simultaneously offers advantages for probing spatiotemporal correlations of fluctuating fields or the dynamics of point defects. In this work, by integrating NVs with foundry silicon-nitride photonic integrated circuits, we realise the scalable operation of eight localised NV-ensemble sensors in an array, with simultaneous, distinct readout of the individual sensors. Using the eight NV sensors and machine-learning methods for multi-point magnetic field reconstruction, we demonstrate microscale magnetic localisation of a 30 μ m-sized needle tip. Experimentally, the needle tip can be localised with an error below its dimension and tracked dynamically with high fidelity. We use simulations of microrobot-relevant magnetic profiles as an application-motivated case study to quantify the operating bounds and requirements for translation and rotation tracking. By moving multi-NV localisation from bulk-optical addressing to a fibre-addressed, guided-wave, multi-channel architecture with simultaneous distinct readout, this work provides a scalable architecture towards magnetic localisation in optically inaccessible environments.

Figures

52 panels with data across 5 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

• panel (g): Normalised NV emission spectrum (NV, blue line) against wavelength Wl. (nm), with the same spectrum multiplied by the waveguide-to-fibre coupling efficiency of the edge couplers (EC, green) and of the grating couplers (GC, orange), both filled down to zero. The print outlines the two filled curves in black. data.csv

Fig. 2

• panel (a-1): PL signal (counts per second) collected from the waveguide of sensor NV 8 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 1 of 8 from the top. data.csv
• panel (a-2): PL signal (counts per second) collected from the waveguide of sensor NV 7 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 2 of 8 from the top. data.csv
• panel (a-3): PL signal (counts per second) collected from the waveguide of sensor NV 6 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 3 of 8 from the top. data.csv
• panel (a-4): PL signal (counts per second) collected from the waveguide of sensor NV 5 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 4 of 8 from the top. data.csv
• panel (a-5): PL signal (counts per second) collected from the waveguide of sensor NV 4 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 5 of 8 from the top. data.csv
• panel (a-6): PL signal (counts per second) collected from the waveguide of sensor NV 3 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 6 of 8 from the top. data.csv
• panel (a-7): PL signal (counts per second) collected from the waveguide of sensor NV 2 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 7 of 8 from the top. data.csv
• panel (a-8): PL signal (counts per second) collected from the waveguide of sensor NV 1 as the excitation fibre array is scanned in X and Y ($\mu$m); X is parallel to the waveguides. The cross marks the fitted centre of the Gaussian spot, which the print labels in $\mu$m. Panel 8 of 8 from the top. data.csv
• panel (b-1): CW ODMR of sensor NV 8 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 1 of 8 from the top. data.csv
• panel (b-2): CW ODMR of sensor NV 7 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 2 of 8 from the top. data.csv
• panel (b-3): CW ODMR of sensor NV 6 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 3 of 8 from the top. data.csv
• panel (b-4): CW ODMR of sensor NV 5 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 4 of 8 from the top. data.csv
• panel (b-5): CW ODMR of sensor NV 4 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 5 of 8 from the top. data.csv
• panel (b-6): CW ODMR of sensor NV 3 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 6 of 8 from the top. data.csv
• panel (b-7): CW ODMR of sensor NV 2 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 7 of 8 from the top. data.csv
• panel (b-8): CW ODMR of sensor NV 1 under zero field: normalized counts against microwave frequency (GHz). Black points joined by a dashed line are the measurement; the red curve is a Gaussian-dip fit. Panel 8 of 8 from the top. data.csv
• panel (c): Measured CW ODMR of one NV-ensemble sensor at three external field strengths: normalised PL against microwave frequency (GHz) for $|B|$ = 0.0, 1.1 and 2.1 mT. Points are the measurement and the curves through them are fits with two Gaussian dips. data.csv
• panel (d): Simulated CW ODMR of an NV ensemble with isotropically distributed orientations: normalised PL against microwave frequency (GHz) for $|B|$ = 0.0, 1.1 and 2.1 mT, the counterpart of the measurement in panel (c). data.csv
• panel (e-1): Zeeman splitting (GHz) of sensor NV 8 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 1 of 8 from the top. data.csv
• panel (e-2): Zeeman splitting (GHz) of sensor NV 7 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 2 of 8 from the top. data.csv
• panel (e-3): Zeeman splitting (GHz) of sensor NV 6 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 3 of 8 from the top. data.csv
• panel (e-4): Zeeman splitting (GHz) of sensor NV 5 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 4 of 8 from the top. data.csv
• panel (e-5): Zeeman splitting (GHz) of sensor NV 4 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 5 of 8 from the top. data.csv
• panel (e-6): Zeeman splitting (GHz) of sensor NV 3 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 6 of 8 from the top. data.csv
• panel (e-7): Zeeman splitting (GHz) of sensor NV 2 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 7 of 8 from the top. data.csv
• panel (e-8): Zeeman splitting (GHz) of sensor NV 1 against the external magnetic field strength (mT). Points are the measurement; the line is a linear fit. Panel 8 of 8 from the top. data.csv
• panel (f-1): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 8 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 1 of 8 from the top. data.csv
• panel (f-2): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 7 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 2 of 8 from the top. data.csv
• panel (f-3): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 6 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 3 of 8 from the top. data.csv
• panel (f-4): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 5 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 4 of 8 from the top. data.csv
• panel (f-5): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 4 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 5 of 8 from the top. data.csv
• panel (f-6): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 3 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 6 of 8 from the top. data.csv
• panel (f-7): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 2 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 7 of 8 from the top. data.csv
• panel (f-8): CW-ODMR sensitivity $\eta_{\mathrm{CW-ODMR}}$ ($\mu$T/$\sqrt{\mathrm{Hz}}$) of sensor NV 1 against the magnetic field strength (mT). Points are the measurement; the curve is taken from the fitted ensemble sensor model. Panel 8 of 8 from the top. data.csv

Fig. 3

• panel (b): Zeeman splitting (GHz) of each of the eight sensors (NV # 1 to 8) for five X positions of the magnetised needle tip, from 1315 to 1565 $\mu$m, drawn as five curves in a 3D box, one per tip X position. data.csv
• panel (c): Zeeman splitting (GHz) of each of the eight sensors (NV # 1 to 8) for five Y positions of the magnetised needle tip, from 1184 to 2200 $\mu$m, drawn as five curves in a 3D box, one per tip Y position. data.csv
• panel (d): True positions (green circles) and estimated positions (pink triangles) of the needle tip in the X-Y plane ($\mu$m), each pair joined by a line. Cyan diamonds are the eight sensor positions and the grey box encloses the experimental operation area. The print leaves the line of one pair undrawn. data.csv
• panel (e): Residuals ($\mu$m) of the estimated needle tip position in panel (d), estimated minus true, for the tip X and the tip Y position. Each point is one test position, with the median and quartile box; the print draws a box plot with whiskers and marks the outliers as circles. data.csv
• panel (f): Average estimation error ($\mu$m) of the needle tip position against the integration time $t$ (s) of the ODMR measurements. Points are the experiment (Exp.) and the curve is a $1/\sqrt{t}$ fit. data.csv
• panel (g): Average estimation error ($\mu$m) of the needle tip position against the training set size $N$. Points are the experiment (Exp.) and the curve is a $1/\sqrt{N}$ fit. data.csv
• panel (h): Average estimation error ($\mu$m) of the needle tip position against the number of sensors used simultaneously. Points are the data and the line is a linear fit (Lin. fit). data.csv

Fig. 4

• panel (a): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 1.8 $\mu$m/minute and a 2.8 mHz frame rate (360 s integration time); the same data as panel (d). data.csv
• panel (b): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 3.5 $\mu$m/minute and a 2.8 mHz frame rate. data.csv
• panel (c): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 7.1 $\mu$m/minute and a 2.8 mHz frame rate. data.csv
• panel (d): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 1.8 $\mu$m/minute and a 2.8 mHz frame rate (360 s integration time); the same data as panel (a). data.csv
• panel (e): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 1.8 $\mu$m/minute and a 5.6 mHz frame rate (180 s integration time). data.csv
• panel (f): Reconstructed trajectory of the needle tip (Rec. trajectory, black points joined in time order) over the true trajectory (red line) in the Y-X plane ($\mu$m), for a tip effective moving speed of 1.8 $\mu$m/minute and a 11.1 mHz frame rate (90 s integration time). data.csv

Fig. 5

• panel (b): Simulated error map of microrobot magnetic localisation with eight NV-ensemble sensors: estimation error ($\mu$m, logarithmic colour scale) against the robot X and Y position ($\mu$m). The black contour marks an estimation error of 50 $\mu$m and the cyan diamonds are the sensor positions. The colour is the base-10 logarithm of the error. data.csv
• panel (c): Y-averaged estimation error ($\mu$m, red bars, left axis) and averaged magnetic field gradient at the sensor locations (mT/$\mu$m, blue bars, right axis) for nine bins of the robot X position ($\mu$m). The dashed vertical line is at $x = -750$ $\mu$m. data.csv
• panel (d): Simulated position tracking of the microrobot along a trajectory with eight single NV sensors, seen from above: true trajectory (True, blue) and estimated trajectory (Est., red) in the robot Y-X plane ($\mu$m), with the single NV sensor positions as cyan diamonds. The print draws this as a 3D box viewed along the Z axis, without tick labels. data.csv
• panel (e): Simulated monitoring of the microrobot orientation along its trajectory with single NV sensors, in a 3D box of robot X, Y and Z position ($\mu$m): true (True, blue) and estimated (Est., red) positions for every second point, each with its orientation as a line of fixed length starting at the point. The print draws the orientations as arrows and prints no tick labels. data.csv

Cite

Hao-Cheng Weng, John G. Rarity, Krishna C. Balram, Joe A. Smith. Photonic-integrated quantum sensor array for microscale magnetic localisation. Nat. Commun. 17, 6185 (2026). https://doi.org/10.1038/s41467-026-73701-0

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