Entanglement-Enhanced Optical Ion Clock

Phys. Rev. Lett. 136, 073601 (2026) · DOI: 10.1103/dyqm-k8p6 · arXiv: 2506.11810

License: CC BY 4.0.

Abstract

Entangled states hold the promise of improving the precision and accuracy of quantum sensors. We experimentally demonstrate that spectroscopy of an optical clock transition using entangled states can outperform its classical counterpart. Two $^{40}$Ca$^+$ ions are entangled in a quantum state with vanishing first-order magnetic field sensitivity, extending the coherence time of the atoms and enabling near-lifetime-limited probe times of up to 550 ms. In our protocol, entangled ions reach the same instability as uncorrelated ions, but at half the probe time, enabling faster cycle times of the clock. We run two entangled $^{40}$Ca$^+$ ions as an optical clock and compare its frequency instability with a $^{87}$Sr lattice clock. The instability of the entangled ion clock is below a clock operated with classically correlated states for all probe times. We observe instabilities below the theoretically expected quantum projection noise limit of two uncorrelated ions for interrogation times below 100 ms. The lowest fractional frequency instability of $7\times 10^{-16}/\sqrt{\tau/1\,\mathrm{s}}$ is reached for 250 ms probe time, limited by residual phase noise of the probe laser. This represents the lowest instability reported to date for a $^{40}$Ca$^+$ ion clock.

Figures

6 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 (1): Contrast of measurement signal against interrogation time (ms) for enDFS (red), ccDFS (blue) and single-ion Ramsey (black), with error bars. Dash-dotted and dotted curves are the lifetime-limited contrast for enDFS and ccDFS; the black curve is a Gaussian noise model. The printed axis break between about 4 and 50 ms is not kept, and the open ccDFS marker at 3.5 ms is drawn filled. data.csv

Fig. 3

• panel (1): Fractional stability of the $^{40}\mathrm{Ca}^+/^{87}\mathrm{Sr}$ frequency ratio, OADEV $\sigma_y$ against averaging time $\tau$ (s), at 50 ms interrogation time for the enDFS (red) and ccDFS (blue) schemes. Filled markers are the data range taken for the stability fit, open markers the rest. Error bars are smaller than the symbols and are not drawn. data.csv
• panel (2): Fractional stability of the $^{40}\mathrm{Ca}^+/^{87}\mathrm{Sr}$ frequency ratio, OADEV $\sigma_y$ against averaging time $\tau$ (s), at 100 ms interrogation time for the enDFS (red) and ccDFS (blue) schemes. Filled markers are the data range taken for the stability fit, open markers the rest. Error bars are smaller than the symbols and are not drawn. data.csv
• panel (3): Fractional stability of the $^{40}\mathrm{Ca}^+/^{87}\mathrm{Sr}$ frequency ratio, OADEV $\sigma_y$ against averaging time $\tau$ (s), at 250 ms interrogation time for the enDFS (red) and ccDFS (blue) schemes. Filled markers are the data range taken for the stability fit, open markers the rest; as printed, ccDFS has no markers at $\tau = 9$, 12 and 16 s. Error bars are smaller than the symbols. data.csv
• panel (4): Fractional stability of the $^{40}\mathrm{Ca}^+/^{87}\mathrm{Sr}$ frequency ratio, OADEV $\sigma_y$ against averaging time $\tau$ (s), at 550 ms interrogation time for the enDFS (red) and ccDFS (blue) schemes. Filled markers are the data range taken for the stability fit, open markers the rest. Error bars are smaller than the symbols and are not drawn. data.csv

Fig. 4

• panel (1): Measured $\sigma_y(\tau = 1\,\mathrm{s})$ against interrogation time $T_{int}$ (s) for enDFS (red) and ccDFS (blue), with error bars, and the quantum projection noise limits for Ramsey (N=1) (dashed), Ramsey (N=2), ccDFS and enDFS. Shaded bands are the expected stabilities, printed in gray and tinted here in the series colors. The printed blue and red regime shading is not shown. data.csv

Cite

Kai Dietze et al. (14 authors). Entanglement-Enhanced Optical Ion Clock. Phys. Rev. Lett. 136, 073601 (2026). https://doi.org/10.1103/dyqm-k8p6

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