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Differential clock comparisons with a multiplexed optical lattice clock


Rapid progress in optical atomic clock performance has advanced the frontiers of timekeeping, metrology and quantum science1,2,3. Despite considerable efforts, the instabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves4,5. Here we implement a ‘multiplexed’ one-dimensional optical lattice clock, in which spatially resolved strontium atom ensembles are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser and read-out in parallel. In synchronous Ramsey interrogations of ensemble pairs we observe atom–atom coherence times of 26 s, a 270-fold improvement over the measured atom–laser coherence time, demonstrate a relative instability of \(9.7(4)\times {10}^{-18}/\sqrt{\tau }\) (where τ is the averaging time) and reach a relative statistical uncertainty of 8.9 × 10−20 after 3.3 h of averaging. These results demonstrate that applications involving optical clock comparisons need not be limited by the instability of the local oscillator. We further realize a miniaturized clock network consisting of 6 atomic ensembles and 15 simultaneous pairwise comparisons with relative instabilities below \(3\times {10}^{-17}/\sqrt{\tau }\), and prepare spatially resolved, heterogeneous ensemble pairs of all four stable strontium isotopes. These results pave the way for multiplexed precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, the development of clock-based gravitational wave and dark matter detectors6,7,8,9,10,11,12 and new tests of relativity in the lab13,14,15,16.

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Fig. 1: Multiplexed OLC configuration and procedure for loading two ensembles.
Fig. 2: Characterization of atom–atom coherence time by synchronous clock comparisons.
Fig. 3: Low relative instability with multiplexed Ramsey interrogation.
Fig. 4: Prospects for multiplexed OLC comparisons.

Data availability

The experimental data presented in this manuscript are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The code used for experimental control, data analysis and simulation in this work are available from the corresponding author upon reasonable request.


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We thank J. Ye, A. Kaufman, J. Thompson, T. Bothwell and A. Jayich for insightful discussions and helpful feedback on the manuscript. This work was supported in part by the NIST Precision Measurement Grants program, the Northwestern University Center for Fundamental Physics and the John Templeton Foundation through a Fundamental Physics grant, the Wisconsin Alumni Research Foundation, the Army Research Office through agreement number W911NF-21-1-0012 and a Packard Fellowship for Science and Engineering.

Author information

Authors and Affiliations



X.Z. designed and built the experimental apparatus with assistance from J.D., V.L., H.L. and B.N.M., and with guidance from S.K. All authors contributed to maintenance and operation of the experimental apparatus, data collection, data analysis and writing of the manuscript.

Corresponding author

Correspondence to Shimon Kolkowitz.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Lattice and clock path.

Schematic diagram showing the lattice and clock beam paths for the interrogation the \(|{}^{1}{S}_{0},{m}_{F}=\pm 5/2\rangle \leftrightarrow |{}^{3}{P}_{0},{m}_{F}=\pm 3/2\rangle \sigma \)-transition. To interrogate the \(|{}^{1}{S}_{0},{m}_{F}=\pm 9/2\rangle \leftrightarrow |{}^{3}{P}_{0},{m}_{F}=\pm 9/2\rangle \)-transition, the first order diffraction clock beam is overlapped with the lattice by first using a long-pass dichroic beam splitter and subsequently transmitting through the polarized beam splitter, shown in the dashed blue box. The inset shows the corresponding orientations of the bias magnetic field (B) and the lattice and clock polarizations (ε). Abbreviations: PBS, polarized beam-splitter; DBS, dichroic beam-splitter; AOM, acousto-optic-modulator; PD, photo-diode; HWP, half-waveplate; QWP, quarter-waveplate.

Extended Data Fig. 2 Energy levels diagram.

a, Energy level diagram for strontium. The double-arrow lines correspond to the relevant transitions, including the 461-nm 1S01P1 transition for the first-stage MOT and imaging, the 689-nm 1S03P1 transition for narrow-linewidth MOT, spin-polarization and in-lattice-cooling, the 679-nm 3P03S1 and 707-nm 3P23S1 transitions for repumping, and the 698-nm 1S03P0 transition for clock interrogation. The wavy lines correspond to spontaneous emission. b, Hyperfine clock states. Red double arrows represent clock interrogation of the \(|{}^{1}{S}_{0},{m}_{F}=\pm 9/2\rangle \leftrightarrow |{}^{3}{P}_{0},{m}_{F}=\pm 9/2\rangle \) transition. Blue double arrows represent clock interrogation of the \(|{}^{1}{S}_{0},{m}_{F}=\pm 5/2\rangle \leftrightarrow |{}^{3}{P}_{0},{m}_{F}=\pm 3/2\rangle \) transition. Grey dashed lines stand for transitions for coherent transfer of atoms from \(|{}^{1}{S}_{0},{m}_{F}=\pm 9/2\rangle \) states to \(|{}^{3}{P}_{0},{m}_{F}=\pm 3/2\rangle \) states.

Extended Data Fig. 3 Timing diagram.

a, Typical timing diagram for a Ramsey spectroscopy sequence, in which laser cooling, state preparation and camera imaging contribute to about 1.6 s dead time, with clock interrogation time ranging from 10 ms to 20 s. b, c, The corresponding lattice retro detuning, lattice velocity and lattice acceleration for loading two ensembles at 1 cm separation.

Extended Data Fig. 4 Comparison of bias correction.

a, b, Comparison of ‘closed-loop’ analysis with (a) and without (b) bias correction. 197 unique ‘closed-loop’ combinations are shown, with each datum corresponds to the sum frequency within each loop. Shaded area represents a window of 1 × 10−18.

Source data

Extended Data Fig. 5 Differential density shift.

a, Measured differential density shift as a function of atom number difference between two symmetrically prepared ensembles at 1 cm separation. The data is taken at 20 Erec lattice trap depth with 6 s interrogation time. Dashed line is the linear fitting, in which the slope is extracted as −8.5(6) × 10−19 shift per 100 atom number difference. b, Scaling of differential density shift per 100 atom number difference between ensemble pairs with lattice trap depth U. The dashed line is a fit to the expected αU5/4 + β scaling20, where α and β are fit parameters.

Source data

Extended Data Table 1 Measured coherence times
Extended Data Table 2 Differential frequencies from 6 ensemble measurement

Supplementary information

Supplementary Information

This file contains Supplementary Information, including Supplementary Figs. 1–8 and additional references.

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Zheng, X., Dolde, J., Lochab, V. et al. Differential clock comparisons with a multiplexed optical lattice clock. Nature 602, 425–430 (2022).

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