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Physical Review Letters

Atomic Coherence of 2 Minutes and Instability of 1.5 × 10 − 18 at 1 s in a Wannier-Stark Lattice Clock

Kyungtae Kim, Alexander Aeppli, William Warfield, Anjun Chu, Ana María Rey, Jun Ye

Published Aug 1, 2025• 11 citations
Publisher

Abstract

We explore the limits of atomic coherence and measurement precision in a ^{87}Sr optical lattice clock. We perform a detailed characterization of key effects, including lattice Raman scattering and atomic collisions in a shallow lattice configuration, determining a 174(28) s ^{3}P_{0} clock state lifetime. Investigation of atomic coherence across a range of lattice depths and atomic densities reveals decoherence mechanisms related to photon scattering and atomic interaction. At a reduced density, we observe a coherence time of 118(9) s, approaching the fundamental limit set by spontaneous emission. Guided by this coherence understanding, we demonstrate a clock instability for an atomic ensemble of 1.5×10^{-18} at 1 s in fractional frequency units. Our results are important for further advancing the state of the art of an optical lattice clock for fundamental physics applications.

DOI
10.1103/3wtv-sty2

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We explore the limits of atomic coherence and measurement precision in a ^{87}Sr optical lattice clock. We perform a detailed characterization of key effects, including lattice Raman scattering and atomic collisions in a shallow lattice configuration, determining a 174(28) s ^{3}P_{0} clock state lifetime. Investigation of atomic coherence across a range of lattice depths and atomic densities reveals decoherence mechanisms related to photon scattering and atomic interaction. At a reduced density, we observe a coherence time of 118(9) s, approaching the fundamental limit set by spontaneous emission. Guided by this coherence understanding, we demonstrate a clock instability for an atomic ensemble of 1.5×10^{-18} at 1 s in fractional frequency units. Our results are important for further advancing the state of the art of an optical lattice clock for fundamental physics applications.
We explore the limits of atomic coherence and measurement precision in a 87Sr optical lattice clock. We perform a detailed characterization of key effects, including lattice Raman scattering and atomic collisions in a shallow lattice configuration, determining a 174(28) s 3P0 clock state lifetime. Investigation of atomic coherence across a range of lattice depths and atomic densities reveals decoherence mechanisms related to photon scattering and atomic interaction. At a reduced density, we observe a coherence time of 118(9) s, approaching the fundamental limit set by spontaneous emission. Guided by this coherence understanding, we demonstrate a clock instability of 1.5E-18 at 1 s in fractional frequency units. Our results are important for further advancing the state-of-the-art of an optical lattice clock for fundamental physics applications.
Increasing coherent interrogation times is central to advancing the precision of optical clocks. Synchronous differential optical clock comparisons have now demonstrated atomic coherence times that far exceed the coherence time of the clock laser. While atom coherence times are then primarily limited by errors induced by lattice Raman scattering, excited clock state radiative decay, and broadening from two-body collisions, many of these errors take the atoms out of the clock transition subspace, and can therefore be converted into “erasure” errors if the appropriate readout scheme is employed. Here we experimentally demonstrate a hyperfine-resolved readout technique for 87 Sr optical lattice clocks that mitigates decoherence from Raman scattering induced by the lattice as well as radiative decay. By employing hyperfine-resolved readout in synchronous differential comparisons between 87 Sr ensembles with both Ramsey and spin-echo spectroscopy sequences, we achieve enhanced atomic coherence times exceeding 100 and 150 s, respectively, enabling longer coherent measurements without a reduction in performance. We anticipate that this hyperfine-resolved readout technique will benefit applications of state-of-the-art optical lattice clock comparisons in which the coherence times are constrained by Raman scattering or radiative decay.
Off-resonant scattering of lattice laser radiation by 87{}^{87}87Sr atoms in the two states 1S0{}^{1}{S}_{0}1S0​ and 3P0{}^{3}{P}_{0}3P0​ and its effect on clock operation are investigated. It is found that Raman scattering eventually limits the achievable frequency instability and thus limits the useful interrogation time in optical lattice clocks at presently used lattice depths.
We investigate the effects of stimulated scattering of optical lattice photons on atomic coherence times in a state-of-the art ^{87}Sr optical lattice clock. Such scattering processes are found to limit the achievable coherence times to less than 12 s (corresponding to a quality factor of 1×10^{16}), significantly shorter than the predicted 145(40) s lifetime of ^{87}Sr's excited clock state. We suggest that shallow, state-independent optical lattices with increased lattice constants can give rise to sufficiently small lattice photon scattering and motional dephasing rates as to enable coherence times on the order of the clock transition's natural lifetime. Not only should this scheme be compatible with the relatively high atomic density associated with Fermi-degenerate gases in three-dimensional optical lattices, but we anticipate that certain properties of various quantum states of matter-such as the localization of atoms in a Mott insulator-can be used to suppress dephasing due to tunneling.
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 report an optical lattice clock with a total systematic uncertainty of 8.1×10^{-19} in fractional frequency units, representing the lowest uncertainty of any clock to date. The clock relies on interrogating the ultranarrow ^{1}S_{0}→^{3}P_{0} transition in a dilute ensemble of fermionic strontium atoms trapped in a vertically-oriented, shallow, one-dimensional optical lattice. Using imaging spectroscopy, we previously demonstrated record high atomic coherence time and measurement precision enabled by precise control of collisional shifts and the lattice light shift. In this work, we revise the black body radiation shift correction by evaluating the 5s4d ^{3}D_{1} lifetime, necessitating precise characterization and control of many body effects in the 5s4d ^{3}D_{1} decay. Last, we measure the second order Zeeman coefficient on the least magnetically sensitive clock transition. All other systematic effects have uncertainties below 1×10^{-19}.