Readout of a solid state spin ensemble at the projection noise limit

Nat. Commun. 17, 4028 (2026) · DOI: 10.1038/s41467-026-72721-0 · arXiv: 2509.11854

License: CC BY 4.0.

Abstract

Spin ensembles are central to quantum science, from fundamental physics searches to magnetic resonance spectroscopy and quantum sensing. The standard quantum limit for their performance is ultimately posed by spin projection noise, yet solid-state implementations have so far been limited by significantly larger photon shot noise. Here, we demonstrate a direct quantum non-demolition readout of a mesoscopic ensemble of nitrogen-vacancy (NV) centers in diamond that surpasses the photon shot-noise limit and approaches the intrinsic spin projection noise. By stabilizing the intrinsic $^{14}$N nuclear spin bath at high magnetic fields and employing a repetitive nuclear-assisted spin readout, we achieve a noise reduction of 3.8 dB below the thermal projection noise level. This enables direct access to the intrinsic fluctuations of the spin ensemble, allowing us to directly observe the signatures of correlated spin states. Our results establish projection noise-limited readout as a practical tool for solid-state quantum sensors, opening pathways to quantum-enhanced metrology, direct detection of many-body correlations, and the implementation of spin squeezing in mesoscopic solid-state ensembles.

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

• panel (a): ODMR spectrum of the NV center: relative number of detected photons against microwave frequency (MHz). The fitted envelope and the readout positions $a$, $b$ and $r$ marked on the printed panel are not drawn. data.csv
• panel (c): Histogram of the photon count difference $b - a$ over 3000 experiments: normalized number of events against photon count difference $b - a$. The second top axis of the printed panel, in normalized counts $(b-a)/2nc$, is not drawn. data.csv
• panel (d): Normalized distribution width $\sigma'$ against number of photons $n$, on log-log axes, with four series: Data, Model, Spin-Projection-Noise and Photon-Shot-Noise. Error bars on Data and Photon-Shot-Noise are the standard error of the mean. The second top axis of the printed panel, readout repetitions $m$, is not drawn. data.csv

Fig. 3

• panel (a-2): Right sub-plot of printed panel (a): photon count difference $b - a$ against RF pulse duration $\tau_{\mathrm{RF}}$ ($\mu$s), coloured by the relative number of events, each column a readout histogram. The two histograms printed beside the map, at $\tau_{\mathrm{RF}} = 0$ and 450 $\mu$s, and the two dashed horizontal guides on the map are not shown. data.csv
• panel (b-1): Upper sub-plot of panel (b): mean spin state $\langle \tilde J_z \rangle$ against RF pulse duration $\tau_{\mathrm{RF}}$ ($\mu$s), with standard-error bars. The three vertical guide lines of the printed panel are drawn. data.csv
• panel (b-2): Lower sub-plot of panel (b): spin distribution width $\sigma_{\tilde J_z}$ against RF pulse duration $\tau_{\mathrm{RF}}$ ($\mu$s), measured (Exp, with standard-error bars) and the Model curve $\sigma^2_{\tilde J_z} \propto p(1-p)$, where $p$ is the readout probability of the nitrogen eigenstates. The three vertical guide lines of the printed panel are drawn. data.csv

Fig. 4

• panel (a-1): Polarized-state histogram of printed panel (a): number of events against Normalized Counts. The print stacks the Polarized, Thermal and Spatially correlated histograms on one axis with vertical offsets; each is its own panel here, without offset. data.csv
• panel (a-2): Thermal-state histogram of printed panel (a): number of events against Normalized Counts. The print stacks the Polarized, Thermal and Spatially correlated histograms on one axis with vertical offsets; each is its own panel here, without offset. data.csv
• panel (a-3): Spatially correlated state histogram of printed panel (a): number of events against Normalized Counts. The print stacks the Polarized, Thermal and Spatially correlated histograms on one axis with vertical offsets; each is its own panel here, without offset. data.csv
• panel (b-1): Upper sub-plot of panel (b): mean spin state $\langle \tilde J_z \rangle$ against normalized time $\tau/T_1$ for spin decay by natural $T_1$ processes ($T_1^{\mathrm{natural}}$) and by a noisy MW drive ($T_1^{\mathrm{noise}}$), lines joining the points, with standard-error bars. data.csv
• panel (b-2): Lower sub-plot of panel (b): spin distribution width $\sigma_{\tilde J_z}$ against normalized time $\tau/T_1$ for $T_1^{\mathrm{natural}}$ and $T_1^{\mathrm{noise}}$, with standard-error bars. Three dashed horizontal lines mark the Correlated, Thermal (uncorrelated) and Polarized levels. data.csv
• panel (c-2): Lower sub-plot of panel (c): spin distribution widths $\sigma_{\tilde J_x}$ and $\sigma_{\tilde J_y}$ against $\tau$ ($\mu$s) for an applied RF field at $f = 250$ kHz, with standard-error bars and the fit to $\sigma_{\tilde J_x}$. Lines mark A (off-resonant) and B (resonant). The printed $\sigma_{\tilde J_z}$ series and fit to $\sigma_{\tilde J_y}$ are not shown. data.csv

Fig. 5

• panel (a): Calculated sensitivity ratio $\eta_{\mathrm{conv}}/\eta_{\mathrm{rep}}$ against number of readouts $m$ and sensing time $\tau_{\mathrm{sens}}$ ($\mu$s), on log-log axes, with the colour bar in powers of ten. The dashed line marks $\tau_{\mathrm{sens}} = 15$ $\mu$s. The black curve of the optimum $m$ in the printed panel is not drawn. data.csv
• panel (b): Calculated sensitivity $\eta$ (T$/\sqrt{\mathrm{Hz}}$) against number of readouts $m$, on log-log axes, for $N_{\mathrm{NV}} = 100$ and $\tau_{\mathrm{sens}} = 1$ ms without squeezing ($\xi^2 = 0.0$ dB). The four squeezed curves, the $\eta_{\mathrm{conv}}$ reference line and the dashed limit lines of the printed panel are not shown. data.csv

Cite

Rouven Maier, Cheng-I Ho, Andrej Denisenko, Marina Davydova, Peter Knittel, Jörg Wrachtrup, Vadim Vorobyov. Readout of a solid state spin ensemble at the projection noise limit. Nat. Commun. 17, 4028 (2026). https://doi.org/10.1038/s41467-026-72721-0

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