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arXiv:2610.17499

An Aubry-André localized optical lattice clock

Shuo Ma, Anke Stölzel, Bennett Christensen, Zhuoli Ding, Dhruva Ganapathy, Andrew Householder, Genyue Liu, Shimon Kolkowitz

physics.atom-phquant-phSubmitted Oct 12, 2026• Announced Oct 14, 2026• 0 citations
v1 · Oct 12, 2026v2 · Oct 14, 2026
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Abstract

Optical lattice clocks in space could improve satellite navigation systems and enable new tests of fundamental physics, including gravitational-wave detection and tests of relativity. In microgravity, atoms can tunnel to degenerate neighboring lattice sites, broadening the clock transition and limiting coherence times. We demonstrate Aubry-André localization in a bichromatic optical lattice formed by two magic-wavelength lasers, suppressing tunneling in a horizontal lattice clock emulating free fall. We recover a Fourier-limited clock Rabi spectrum and measure Ramsey coherence times of up to 2 s in shallow lattices, with up to 100-fold improvement over the delocalized regime. These results establish Aubry-André localization as a practical route to controlling tunneling in future space-based clocks, and open a path to operating terrestrial clocks at shallower lattice depths.

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Optical lattice clocks in space could improve satellite navigation systems and enable new tests of fundamental physics, including gravitational-wave detection and tests of relativity. In microgravity, atoms can tunnel to degenerate neighboring lattice sites, broadening the clock transition and limiting coherence times. We demonstrate Aubry-André localization in a bichromatic optical lattice formed by two magic-wavelength lasers, suppressing tunneling in a horizontal lattice clock emulating free fall. We recover a Fourier-limited clock Rabi spectrum and measure Ramsey coherence times of up to 2 s in shallow lattices, with up to 100-fold improvement over the delocalized regime. These results establish Aubry-André localization as a practical route to controlling tunneling in future space-based clocks, and open a path to operating terrestrial clocks at shallower lattice depths.
Rapid progress in the precision and accuracy of optical atomic clocks over the last decade has advanced the frontiers of timekeeping, metrology, and quantum science. However, the stabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves, leaving room for further progress. Here we implement a "multiplexed" one-dimensional optical lattice clock, in which spatially-resolved, movable ensembles of ultra-cold strontium atoms are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser, and read-out in parallel. By performing synchronized Ramsey interrogations of ensemble pairs we observe atom-atom coherence times up to 26 seconds, a 270-fold improvement over the atom-laser coherence time, demonstrate a relative stability of 9.7(4)×10−18/τ9.7(4)\times10^{-18}/\sqrtτ9.7(4)×10−18/τ​ (where τττ is the averaging time in seconds), and reach a fractional uncertainty of 8.9(3)×10−208.9(3)\times 10^{-20}8.9(3)×10−20 after 3.3 hours of averaging. These results demonstrate that applications requiring ultra-high-precision comparisons between optical atomic clocks need not be limited by the stability of the local oscillator. With multiple ensemble pairs, we realize a miniaturized clock network consisting of 6 atom ensembles, resulting in 15 unique pairwise clock comparisons with relative stabilities below 3×10−17/τ3\times10^{-17}/\sqrtτ3×10−17/τ​. Finally, we demonstrate the capability to simultaneously load spatially-resolved, heterogeneous ensemble pairs of all four stable isotopes of strontium in a lattice. The unique capabilities offered by this platform pave the way for future studies of precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, development of clock-based gravitational wave and dark matter detectors, and novel tests of relativity including measurements of the gravitational redshift at sub-centimeter scales.
We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunneling leads to a residual sensitivity to the atom dynamics hence requiring large depths [(50–100)Er(50\text{--}100){E}_{r}(50–100)Er​ for Sr] to avoid any frequency shift or line broadening of the atomic transition at the ${10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g., higher-order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunneling. We show that using the Earth's gravity, much shallower traps (down to 5Er5{E}_{r}5Er​ for Sr) can be used for the same accuracy goal.
Optical atomic clocks have spurred a range of precision frequency comparison experiments and proposals including tests of general relativity, gravitational wave detection, and relativistic geodesy. Current measurements using optical atomic clocks are often limited by the coherence of the clock laser rather than the atomic samples used as a frequency reference. In order to overcome the performance limits imposed by clock laser coherence, we realize a multiplexed optical clock system where multiple spatially resolved ensembles each consisting of thousands of strontium atoms trapped in a 1D optical lattice function as separate atomic frequency references that can be simultaneously interrogated with a shared clock laser. This scheme allows us to make differential frequency comparisons with a quantum projection noise limited fractional instability of 9.7(4)×10−18/ √τ and a differential fractional uncertainty of 8.9×10−20 after 3.3 hours of averaging. We then use this system to perform a lab-based test of the gravitational redshift at the centimeter scale, where we measure a fractional frequency gradient of [−12.4±0.7stat ±2.5sys]×10−19/cm, consistent with the predicted value of 10.9×10−19/cm. Having demonstrated that our differential comparisons are no longer limited by the local oscillator, we turn to fundamental limits on atom–atom coherence. We perform a direct decay measurement of the natural lifetime of the excited clock state 3P0 in 87Sr, in which we use measurements of simultaneously loaded high and low density atomic ensembles and compare decay rates of 87Sr and 88Sr to help isolate natural lifetime decay from other population dynamics. We measure a lifetime of 167+79 −40, which is consistent with previously reported experimental and theoretical values. Lastly, we demonstrate a hyperfine-resolved readout scheme in 87Sr that converts depolarization errors during interrogation into erasure errors, extending coherence times between ensembles in our optical lattice clock up to 150s using spin-echo measurements. These results taken together demonstrate the advantages of differential clock measurements that aren’t limited by clock laser coherence and how to characterize and improve on the performance limits that arise in that regime.
We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunnelling leads to a residual sensitivity to the atom dynamics hence requiring large depths (50 to 100 Erfor Sr) to avoid any frequency shift or line broadening of the atomic transition at the 10-17- 10-18level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g. higher order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunnelling. We show that using the Earth's gravity, much shallower traps (down to 5 Erfor Sr) can be used for the same accuracy goal
The quantum metrology with ultra-high precision usually requires the atoms prepared in an ultra-stable environment with well-defined quantum states. Thus, the optical lattice clock system chooses deep lattice potential to trap the ultra-cold atoms. However, building atomic clock in shallow optical lattice can greatly reduce decoherence rate induced by Raman scattering as well as higher order light shift, but tunneling among the lattice sites will cause additional dephasing and strongly broadening of the Rabi spectrum. Here, we periodically drive the shallow 87^{87}87Sr optical lattice clock in the experiment. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz line-width. With careful comparison between the theory and experiment, we demonstrate the Rabi frequency and Bloch bands can be simultaneously and independently tuned by adjusting the driving frequency and amplitude. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phase of matter, such as engineering exotic spin orbit coupling Hamiltonian.
Optical clocks operated on satellites are expected to open up new opportunities in time transfer, geodesy, fundamental physics, and satellite navigation. Here we demonstrate an important first step towards this goal: a modular, compact, optical lattice clock (OLC) system that achieves $2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty. The clock is operated with bosonic strontium and improves the performance of bosonic OLCs by a factor of 30. This has important implications for future use of bosonic OLCs in fundamental physics and metrology. We make use of the clock's metrological performance to measure, with independent clocks, the isotope shift of the $^{1}S_{0}\ensuremath{\rightarrow}^{3}P_{0}$ transitions of 88Sr^{88}\mathrm{Sr}88Sr and 87Sr^{87}\mathrm{Sr}87Sr, with an uncertainty of 12 mHz. The ratio of the transition frequencies is thus determined with $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ fractional uncertainty.