Wideband covariance magnetometry below the diffraction limit

TL;DR

The work demonstrates wideband, sub-diffraction-limit magnetometry using a pair of NV centers to measure correlations of magnetic noise across MHz–GHz bands. By combining independent NV addressing, resonant/RA-SCC readout, and tailored sensing sequences, the authors extract cross-correlations via Pearson metrics and relate them to the cross-spectral density $S_{12}(\omega)$, enabling characterization of nonlocal magnetic noise sources. A comprehensive theoretical framework—covering driven correlations, $T_2$- and $T_1$-type spectroscopy, and Markovian dephasing with correlated noise—supports quantitative fitting of the data and separation of local vs. shared noise contributions. The approach provides a powerful tool for probing condensed-matter phenomena with nonlocal correlations and high-frequency noise, potentially enabling new insights into correlated spin systems and nanoscale magnetometry beyond the diffraction limit.

Abstract

We experimentally demonstrate a method for measuring correlations of wideband magnetic signals with spatial resolution below the optical diffraction limit. Our technique employs two nitrogen-vacancy (NV) centers in diamond as nanoscale magnetometers, spectrally resolved by inhomogeneous optical transitions. Using high-fidelity optical readout and long spin coherence time, we probe correlated MHz-range noise with sensitivity of 15 nT Hz$^{-1/4}$. In addition, we use this system for correlated $T_1$ relaxometry, enabling correlation measurements of GHz-range noise. Under such externally applied noise, while individual NV centers exhibit featureless relaxation, their correlation displays rich coherent and incoherent dynamics reminiscent of superradiance physics. This capability to probe high-frequency correlations provides a powerful tool for investigating a variety of condensed-matter phenomena characterized by nonlocal correlations.

Figures (10)

• Figure S1: ODMR spectrum taken with conventional green readout, showing distinct MW transitions for each NV. As in the main text, blue (red) denotes NV1 (NV2) throughout the Supplemental Material unless noted otherwise.
• Figure S2: Effects of optical power on resonant readout. (a) Saturation curves with fits (solid lines). (b) Power broadening of the linewidths. Dashed lines are guides to the eye.
• Figure S3: Resonant readout duration for NV1 (a) and NV2 (b). Without MW excitations during readout, the available collection window is very short ($< 5\,$µ s) for both high and low optical power (circle datapoints, fitted with dashed curves). With low-power ($f_{\rm Rabi}\approx 2\,$MHz) MW excitations during readout to mix the spin states (triangles, solid curves), the NVs can be read for milliseconds (insets).
• Figure S4: RA-SCC readout noise versus ionization time (a) and initialization time (b). The NVs can be ionized at the same time ("co-izn.") or independently ("indep."). All curves are guides to the eye. Grey area denotes the parameter range used for correlation measurements.
• Figure S5: Minimum detectable correlated magnetic field as calculated for different readout methods. For conventional readout ("conv.", dashed green), we assume the initialization time $t_{\rm init} = 5\,$µ s, phase integration time $t = 10\,$µ s, similar to Fig. 3 of the main text, and readout time $t_{\rm R} = 300\,$ns. For resonant readout ("RR", dashed orange), $t_{\rm init} = 30\,$µ s, $t = 10\,$µ s, and $t_{\rm R} = 2\times2\,$µ s due to sequential reading of each NV. For RA-SCC, we show both cases corresponding to $t = 10\,$µ s (thin solid purple) and $t = T_{\rm 2}/2\,$ (thick solid purple) respectively, with $T_{\rm 2} = 2\,$ms based on Fig. \ref{['fig::figS7']}(a). For both cases, $t_{\rm init} = 1.5\,$ms and $t_{\rm R} = 2\times3\,$ms. The annotations adjacent to each curve indicate magnetic sensitivity of the corresponding readout method. The vertical dashed line denotes the experiment time per datapoint in each curve in Fig. 3(b) of the main text.