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# Improved interspecies optical clock comparisons through differential spectroscopy

## Abstract

Comparisons of high-accuracy optical atomic clocks1 are essential for precision tests of fundamental physics2, relativistic geodesy3,4,5 and the anticipated redefinition of the second by the International System of Units6. The scientific reach of these applications is restricted by the statistical precision of comparison measurements between clocks realized with different atomic species. The instability of individual clocks is limited by the finite coherence time of the optical local oscillator, which bounds the maximum atomic interrogation time. Here we experimentally demonstrate differential spectroscopy7, a comparison protocol that enables interrogating times beyond the optical local oscillator coherence time. By phase coherently linking a zero-dead-time8 Yb optical lattice clock with an Al+ single-ion clock via an optical frequency comb and performing synchronized Ramsey spectroscopy, we show an improvement in comparison instability relative to previous results9 of nearly an order of magnitude. This result represents one of the most stable interspecies clock comparisons to date.

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## Data availability

All the supporting data are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank R. C. Brown and C.-W. Chou for their careful reading and feedback on this manuscript. We also acknowledge contributions from P. Rich, in carrying out a characterization of the magnetic field noise of the Yb system. This work was supported by the National Institute of Standards and Technology (NIST), the Defense Advanced Research Projects Agency (Atomic-Photonic Integration Program), the National Science Foundation Q-SEnSE Quantum Leap Challenge Institute (grant no. 2016244) and the Office of Naval Research (grant nos. N00014-18-1-2634 and N00014-20-1-2431). M.E.K. was supported by an appointment to the Intelligence Community Postdoctoral Research Fellowship Program at NIST administered by ORISE through an interagency agreement between the DOE and ODNI. H.L. was supported by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. The views, opinions and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the US government.

## Author information

Authors

### Contributions

All the authors contributed to the design of the experiment, collection of data and revision of the manuscript. During the measurements, Al+ clock operation was conducted by E.R.C., D.B.H., M.E.K., D.R.L. and J.L.V. Yb clock operation was conducted by W.F.M., Y.S.H., X.Z. and A.D.L. Comb metrology laboratory operation was conducted by T.M.F., H.L. and N.V.N. Data analysis and preparation of the manuscript were performed by M.E.K., D.R.L., W.F.M. and N.V.N.

### Corresponding authors

Correspondence to David B. Hume, Tara M. Fortier, Andrew D. Ludlow or David R. Leibrandt.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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### Peer review information

Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Frequency comb optical path.

Optical paths surrounding the optical frequency comb portion of the experiment that enables coherent transfer of phase between the Yb and Al+ clocks.

### Extended Data Fig. 2 An optimized zero-dead-time clock.

(a) The timing sequence for a ZDT clock with a variable delay between the π/2-pulses. Note that the length of each step is not to scale. (b) Displayed is the sensitivity function for a zero- dead-time sequence in which the Ramsey pulses of the two atomic systems are precisely overlapped (red) or offset from each other by 27.73% (green). The sensitivity functions have been vertically offset from each other for visual clarity. (c) The optimal delay is determined by calculating the one-second Dick instability for a variable delay between the two pulses. These calculations assume the OLO noise is flicker-frequency and at the level of 1.5 × 10-16. The blue line demonstrates that the Dick instability exhibits a sharply defined minimum. We emphasize that the Dick instability reported here would be added in quadrature with other sources of instability, such as atomic detection noise and quantum-projection noise, which under current conditions would limit the total clock instability at a level at least an order of magnitude higher than the calculated Dick instability. The red and green dots represent the conditions with overlapping Ramsey pulses and optimized timing, respectively.

### Extended Data Fig. 3 Instability added by phase-stabilized fibre network.

The Al+ clock OLO, which is locked to the Yb clock OLO through the Er/Yb:glass frequency comb, and the Yb clock OLO are compared with a Ti:Sapphire frequency comb. The top figure shows the histogram of the frequency noise, and the bottom shows the Allan deviation plot.

### Extended Data Fig. 4 Results of the simulations that vary the noise sources in the operation of the ZDT di erential spectroscopy operation.

The top panel shows the contrast in the phase scan of the Al+ clock, and the bottom shows the Allan deviation plot for: when only the OLO noise is present (yellow line), when OLO and the magnetic field noise sources are present (orange line), and when OLO, magnetic field, and the fibre link noises are present (blue line). The green dashed line in the bottom panel indicates the QPN limit.

### Extended Data Fig. 5 Example of the data analysis used to determine the long-averaging-time asymptotic Allan deviation.

This data set is Ramsey spectroscopy of the Al+ clock without any feedforward corrections from Yb, at a interrogation time of 454 ms. The top panel shows the time series of the measured Al+ transition frequency relative to the Yb stabilized OLO. The middle left panel shows the corresponding power spectral density of frequency noise, which is fit to the function $${S}_{w}/(1+{(f/{f}_{c})}^{2})$$. The t residuals are shown at the bottom of this panel. The middle right panel shows χ2 as a function of the two t parameters. The red dotted line is a contour of constant $${\chi }^{2}=\min ({\chi }^{2})+1$$, and the black dashed lines are the 68% confidence interval bounds for the fit parameter Sw. The bottom panel shows the Allan deviation of the frequency data (blue circles) and the long-averaging-time asymptotic Allan deviation corresponding to the Sw fit parameter (red line and shaded confidence interval).

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Kim, M.E., McGrew, W.F., Nardelli, N.V. et al. Improved interspecies optical clock comparisons through differential spectroscopy. Nat. Phys. 19, 25–29 (2023). https://doi.org/10.1038/s41567-022-01794-7

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• DOI: https://doi.org/10.1038/s41567-022-01794-7