Toward a temperature-insensitive composite diamond clock

Phys. Rev. Appl. 25, 064046 (2026) · DOI: 10.1103/z2sl-6gcc · arXiv: 2601.00157

Paper license: CC BY 4.0. Data: Hosted with the authors' permission; no licence granted. Ask the authors before reuse beyond citation.

Abstract

Frequency references based on solid-state spins promise simplicity, compactness, robustness, multifunctionality, ease of integration, and high densities of emitters. Nitrogen-vacancy (NV) centers in diamond are a natural candidate, but the electronic zero-field splitting ($D \approx 2.87$ GHz) exhibits a large fractional temperature dependence (around 25 ppb/mK), which has precluded its use as a stable clock transition. Here we show that this limitation can be overcome by forming a composite frequency reference that combines measurements of the electronic splitting $D$ with the nuclear quadrupole splitting ($Q \approx 4.94$ MHz) of the $^{14}$N nuclear spin intrinsic to the NV center. We further benchmark this composite approach against alternative strategies for mitigating temperature sensitivity, including cryogenic operation, temperature compensation, and active stabilization. By implementing a specially designed pulse sequence with an eight-phase control scheme that suppresses pulse imperfections, we interleave measurements of $D$ and $Q$ in a high-density NV ensemble and demonstrate a temperature-compensated composite frequency reference. The stability of this composite diamond clock is characterized over a 10-day period at room temperature through a comparison to a Rb vapor-cell clock, yielding a fractional instability below $5 \times 10^{-9}$ for an averaging time of $\tau = 200$ s and below $1 \times 10^{-8}$ at $\tau = 2 \times 10^5$ s, corresponding to measured improvements by a factor of approximately 4 and approximately 200, respectively, over a clock based purely on the single frequency $D$ for the same periods. By characterizing the residual sensitivity to magnetic fields, optical power, and radio-frequency drive amplitudes, we find that temperature is no longer the dominant source of instability. These results establish complementary electron- and nuclear-spin transitions in diamond as a viable route to thermally robust frequency metrology, providing a pathway toward compact, multifunctional solid-state clocks and quantum sensors.

Figures

11 panels with data across 3 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 (c-1): Amplitude (dB) against frequency (MHz): the amplitude spectrum of a single-phase measurement (TTZFS-1) on the nuclear spin ($Q$), with $\tau$ scanned. The top plot of panel (c); as in the caption, it is scaled by a factor of eight. Its inset is a separate panel, the peak labels are not drawn, and the hosted amplitudes sit a few dB below the printed ones. data.csv
• panel (c-1-inset): Inset of the top plot of panel (c): change in fluorescence against $\tau$ ($\mu$s) over the first few microseconds of the single-phase (TTZFS-1) measurement on $Q$. Markers are the samples; the line, labelled sinc interpolation, is interpolated between them. data.csv
• panel (c-2): Amplitude (dB) against frequency (MHz): the amplitude spectrum of the combination of 8 phases (TTZFS-8) on the nuclear spin ($Q$), with $\tau$ scanned. The bottom plot of panel (c). Its inset is a separate panel, the peak label is not drawn, and the hosted amplitudes sit a few dB below the printed ones. data.csv
• panel (c-2-inset): Inset of the bottom plot of panel (c): change in fluorescence against $\tau$ ($\mu$s) over the first few microseconds of the combination of 8 phases (TTZFS-8) on $Q$. Markers are the samples; the line, labelled sinc interpolation, is interpolated between them. data.csv
• panel (d-1): Change in fluorescence against free-evolution time $\tau$ (ms) for the TTZFS-8 measurement of $Q$, the top plot of panel (d). Markers are the measured data and the line is the fit, $A\cos(2\pi f\tau + \phi)\,e^{-(\tau/T)^{\beta}} + c$. The printed box with the decay time and stretch factor is not drawn. data.csv
• panel (d-2): Change in fluorescence against free-evolution time $\tau$ ($\mu$s) for the TTZFS-8 measurement of $D$, the bottom plot of panel (d). Markers are the measured data and the line is the fit, $A\cos(2\pi f\tau + \phi)\,e^{-(\tau/T)^{\beta}} + c$. The printed box with the decay time and stretch factor is not drawn. data.csv

Fig. 3

• panel (1): Temperature shift (K) against time ($10^5$ s) over a 10-day period, three series: $\lambda_{D}^{-1}\,(\delta D / D)$, $\lambda_{Q}^{-1}\,(\delta Q / Q)$ and their difference $\sim \delta\psi$. Faint points are a subsample of the individual measurements and solid lines are smoothed curves. The top plot of the figure; its upper axis in days is not drawn. data.csv
• panel (2): Allan deviation $\sigma(t)$ against averaging time $t$ (s), log-log, in fractional units, three series: $\delta D / D$, $\delta Q / Q$ and the composite $\delta \psi / \psi$. Shaded bands are the $\pm 3\hat\sigma$ confidence bounds. The bottom plot of the figure. data.csv

Fig. 4

The underlying data is not available. The figure is shown in the paper PDF.

Fig. 5

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

Fig. 6

• panel (a): Amplitude (dB) against frequency (MHz): the analytically expected spectrum of a single measurement (TTZFS-1) on the nuclear spin ($Q$) with $\tau$ scanned, averaged over a distribution of Rabi frequencies. The peak labels of the printed panel are not drawn. data.csv
• panel (b): Amplitude (dB) against frequency (MHz): the analytically expected spectrum of the eight-phase combination (TTZFS-8) on the nuclear spin ($Q$) with $\tau$ scanned, averaged over a distribution of Rabi frequencies. The peak label of the printed panel is not drawn. data.csv
• panel (c): Amplitude (dB) against frequency (MHz): the analytically expected spectrum of a single measurement on the nuclear spin ($Q$) for a perfect $2\pi$ pulse, TTZFS-1 (ideal-$2\pi$), averaged over a distribution of Rabi frequencies. The peak label of the printed panel is not drawn. data.csv

Cite

Sean Lourette et al. (11 authors). Toward a temperature-insensitive composite diamond clock. Phys. Rev. Appl. 25, 064046 (2026). https://doi.org/10.1103/z2sl-6gcc

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