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Nature Communications

Spatially defined Rabi spectroscopy for uninterrupted optical clock interrogation

Koki Nishida, Ryoto Takeuchi, Shigenori Tsuji, 翔一 岡場, Hidetoshi Katori

Published Aug 6, 2026• 0 citations
Publisher

Abstract

Optical lattice clocks achieve fractional frequency uncertainties of 10⁻¹⁸, yet stability is constrained by the dead time between cooling, preparation, interrogation, and detection. This sampling aliases local-oscillator noise into the clock signal (the Dick effect) and prevents continuous accumulation of oscillator phase information. We demonstrate spatially defined Rabi spectroscopy of ultracold ⁸⁸Sr atoms continuously transported in a moving optical lattice. A longitudinal excitation geometry preserves Lamb-Dicke confinement and suppresses Doppler broadening. Clock excitation is enabled only within a localised region by a transverse magnetic mixing field, defining the atom-laser interaction in space rather than in time and decoupling interrogation from preparation and detection. Transporting atoms at 16 mm s⁻¹ through a 12-mm interaction region yields a 1.2-Hz-wide spectrum close to the transit-time Fourier limit while maintaining uninterrupted atom delivery. This approach provides a practical route toward dead-time-free optical clock interrogation of continuously delivered atomic ensembles.

DOI
10.1038/s41467-026-76017-1

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Optical lattice clocks achieve fractional frequency uncertainties of 10⁻¹⁸, yet stability is constrained by the dead time between cooling, preparation, interrogation, and detection. This sampling aliases local-oscillator noise into the clock signal (the Dick effect) and prevents continuous accumulation of oscillator phase information. We demonstrate spatially defined Rabi spectroscopy of ultracold ⁸⁸Sr atoms continuously transported in a moving optical lattice. A longitudinal excitation geometry preserves Lamb-Dicke confinement and suppresses Doppler broadening. Clock excitation is enabled only within a localised region by a transverse magnetic mixing field, defining the atom-laser interaction in space rather than in time and decoupling interrogation from preparation and detection. Transporting atoms at 16 mm s⁻¹ through a 12-mm interaction region yields a 1.2-Hz-wide spectrum close to the transit-time Fourier limit while maintaining uninterrupted atom delivery. This approach provides a practical route toward dead-time-free optical clock interrogation of continuously delivered atomic ensembles.
Optical atomic clocks play a crucial role in fundamental physics, relativistic geodesy, and the future redefinition of the Systeme International second. Standard operation relies on cyclic interrogation sequences, which alternate between atomic interrogation and dead time used for state preparation and readout. This approach introduces the Dick effect, where laser frequency noise aliases onto the atomic transition frequency. Although reducing laser noise improves clock stability, the Dick effect remains a key limitation. In this Letter, we demonstrate a zero-dead-time optical clock based on two interleaved ensembles of cold ^{87}Sr atoms. Our system significantly suppresses this noise and achieves a fractional frequency instability at the 10^{-19} level between 10 000 and 20 000 s over repeated measurements, with a best value of 2.9×10^{-19} at τ=20000 s. The estimated long-term stability based on the combined data of these measurements reaches 2.5×10^{-19} at 1 day. These results represent a more than ninefold improvement over a conventional single-ensemble clock, highlighting its potential for next-generation timekeeping applications.
Abstract We propose a longitudinal Ramsey spectroscopy of atoms in a moving optical lattice. Spatially separated magnetic fields, which open the forbidden 1 S 0 − 3 P 0 transition by mixing with the dipole-allowed states, create Ramsey pulses for a probe laser introduced along the optical lattice. Excitation of atoms in the Lamb-Dicke regime by a single probe laser avoids residual Doppler effects as well as mechanical instabilities that deteriorate Ramsey spectroscopy on an atomic beam. Continuous measurement and control of the probe laser improves the Allan deviation as τ −1 for an averaging time τ until the quantum projection noise limit is reached. For 88 Sr atoms with an atomic flux of 10 4 s −1 , we speculate a clock instability of 5 × 10 −16 ( τ s −1 ) −1 down to its floor at around 10 −18 .
Frequency metrology underpins precise measurements. At the forefront of this field are optical clocks which can perform measurements that are accurate to more digits than those in the number representing seconds elapsed from the beginning of the universe. Frequency estimation errors in the operation of optical clocks lead to frequency instability, prohibiting them from reaching high accuracies on short to medium time scales, and limiting access to interesting measurements of the atomic environment and exotic external perturbations such as gravity fields or fields of fundamentally new physical origins. Optical lattice traps are typically employed in state-of-the-art optical clocks to suppress Doppler effects. By carefully tuning the optical lattice to the magic wavelength, unwanted Stark shifts can be suppressed significantly, allowing operation with thousands of atoms and minimising the fundamental source of frequency estimation errors, namely the quantum projection noise, to around 3 × 10−17 at 1 s. In this thesis, the status of the two Strontium optical lattice clocks at NPL, Sr1 and Sr2, is presented going over a few interesting measurement campaigns from the past years involving Sr1 and the latest experimental efforts to re-enable operation of Sr2. A model of clock stability is developed by incorporating known and new frameworks to characterise the relation between the operating parameters of optical clocks and their performance, with relevance to the NPL lattice clocks and beyond. In particular, a method is identified for addressing the main technical noise for optical lattice clocks, the Dick effect, which typically has a magnitude of 10−16 at 1 s and prevents optical lattice clocks from reaching the quantum projection noise level. By taking advantage of dynamical decoupling we can engineer an optimised duty cycle with benefits in general for systems limited by the optical coherence of the clock laser. Moreover, a study of other noise sources in the NPL lattice clocks is conducted using synchronous measurements between Sr1 and Sr2, revealing a large contribution from linear Zeeman shifts, also at the 10−16 level, and a plan to tackle them is detailed. A hybrid clock architecture is discussed showing how optical lattice clocks can improve the optical coherence of ion clocks thanks to their higher servo rate, and a preliminary experimental demonstration is reported. Finally, a new type of spectroscopy is presented which completely avoids aliasing of linear Zeeman shifts by simultaneously driving transitions with opposite Zeeman sensitivities. Such a technique also enables the continuous interrogation of atoms, a crucial missing component in the Dick-free conveyor belt lattice clock concept heralded as the next standard of stable optical clocks.
Abstract The clock transition at a wavelength of 1.14 μm in thulium atoms in an optical lattice in the Lamb – Dick regime is studied. The capture of thulium atoms makes it possible to suppress completely both the transition broadening due to the first-order Doppler effect and the shift of the transition frequency caused by the recoil effect. The excitation spectra of sideband oscillation frequencies and Rabi oscillations of population between the clock transition levels upon resonance excitation are investigated.
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 investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep one-dimensional optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi line shapes of the carrier transition, we obtain a model to quantify trap-state-dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows sss-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean-field shift of the clock transition.