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Atomic Coherence of 2 minutes and Instability of 1.5E-18 at 1 s in a Wannier-Stark Lattice Clock

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read In a shallow Wannier-Stark strontium lattice clock, atomic coherence reaches 118(9) seconds at low density and the single-clock instability reaches $1.5\times10^{-18}$ at 1 second.

desk verdict Measured 118 s coherence and 1.5e-18 instability are solid; the 'fundamental limit' extrapolation and an internal error-bar mismatch need attention before publication. read the letter →

arxiv 2505.06444 v1 pith:X7STHMM3 submitted 2025-05-09 physics.atom-ph

Kyungtae Kim , Alexander Aeppli , William Warfield , Anjun Chu , Ana Maria Rey , Jun Ye This is my paper · ORCID
classification physics.atom-ph
keywords opticallatticeclockstrontium-87Wannier-StarkatomiccoherenceRamanscatteringblackbodyradiationinstabilityquantumprojectionnoise
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

An optical lattice clock built from strontium-87 atoms in a shallow, gravity-tilted Wannier-Stark lattice holds atomic coherence for 118(9) seconds at nine atoms per site, close to the fundamental limit set by spontaneous emission and blackbody radiation. The same system reaches a single-clock fractional instability of $1.5\times10^{-18}$ at one second of averaging. The paper establishes how lattice Raman scattering and atomic collisions set these limits: scattered photons create spectator atoms that collide with clock atoms, and this density-dependent decoherence can be pushed down by operating at shallow lattice depth and low density. It also reports a ${}^3P_0$ clock-state lifetime of 174(28) seconds, complementing the coherence measurement. The result matters because it shows that a many-atom clock can approach the atomic lifetime limit while preserving the atom number needed to suppress quantum projection noise.

What carries the argument

The argument runs through three devices: a rate-equation model for population decay that separates single-body loss ($\Gamma_e,\Gamma_g$), Raman pumping ($\Gamma_L$), and two-body inelastic loss ($\tilde\Gamma_{ee}$); a linear density extrapolation $\gamma=\gamma_0+\gamma_N N_{\mathrm{site}}$ that isolates the single-atom coherence rate; and an extrapolation of $\gamma_0$ in lattice depth $U_0$ to zero. A Wannier-Stark lattice, a one-dimensional optical lattice tilted by gravity with roughly 260 $\mu$m site spacing, lets the clock run at only a few recoil energies $E_r$, suppressing Raman scattering, while in-situ imaging spectroscopy with ellipse fitting converts spatial contrast into a frequency-difference estimate for the instability. A dissipative discrete truncated Wigner approximation supplies the theoretical $\gamma_N$ that supports the spectator-atom collision picture.

What would settle it

Measure the zero-density Ramsey contrast decay rate $\gamma_0$ at lattice depths between 10 and 40 $E_r$ and compare it with the extrapolated line: if $\gamma_0$ deviates upward as $U_0$ drops, the lifetime inference is biased. Independently, measure the ${}^3P_0$ lifetime with a single atom in a magic-wavelength trap; agreement with 174(28) s would confirm the population-decay analysis, while a significantly different value would break the link between the measured Raman pumping rate and the fundamental lifetime limit.

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Extended reading notes

Core claim

The paper's central claim is that in a shallow Wannier-Stark lattice of ${}^{87}\mathrm{Sr}$ at $U_0=11E_r$ and $N_{\mathrm{site}}=9$, the Ramsey coherence time reaches 118(9) s, and the inferred zero-density, zero-lattice-depth decoherence rate matches $(\Gamma_{\mathrm{nat}}+\Gamma_{\mathrm{BBR}})/2$, so the clock runs at the fundamental atomic limit. Guided by this understanding, a single clock region demonstrates $\sigma_y(1\,\mathrm{s})=1.5\times10^{-18}$ under $T_{\mathrm{dark}}=7$ s with 313 realizations. The density-dependent decoherence is traced to spectator atoms produced by lattice Raman scattering, which undergo strong s-wave collisions with atoms in the clock state; a dissipative discrete truncated Wigner simulation reproduces the measured $\gamma_N$. The paper argues that the combination of shallow lattice depth and moderate atom number optimally balances Raman scattering, collisional decoherence, and quantum projection noise.

Load-bearing premise

The weakest load-bearing premise is that the straight-line relation between $\gamma_0$ and lattice depth $U_0$, fitted only for $U_0>50E_r$, remains valid down to $U_0=0$; if shallow-lattice dynamics change below $50E_r$, the agreement with $(\Gamma_{\mathrm{nat}}+\Gamma_{\mathrm{BBR}})/2$ and the inferred 174(28) s lifetime would be biased.

Editorial extensions

If this is right

  • The single-clock instability follows $\sigma_y(\tau)=1.5\times10^{-18}/\sqrt{\tau/\mathrm{s}}$ for averaging times up to $10^3$ s, so longer integration continues to improve precision.
  • The measured $\gamma_N$ shows that spectator atoms, not direct excited-state collisions, dominate density-dependent decoherence in deeper lattices; removing those atoms would allow larger atom numbers without paying a coherence penalty.
  • At the zero-lattice-depth limit the decoherence rate is $(\Gamma_{\mathrm{nat}}+\Gamma_{\mathrm{BBR}})/2$, meaning shallow-lattice clocks are limited by the atom's own lifetime and the thermal environment rather than by lattice photons.
  • Operating at $U_0\approx11E_r$ with $N_{\mathrm{site}}\approx9$ balances coherence, atom number, and quantum projection noise, providing a practical operating point for high-stability clocks.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The agreement with $(\Gamma_{\mathrm{nat}}+\Gamma_{\mathrm{BBR}})/2$ is the strongest evidence for the paper's thesis, but it rests on a fit that excludes lattice depths below $50E_r$; direct measurements there would settle whether the extrapolation is valid.
  • If spectator atoms are the main density-dependent decoherence channel, then detecting and removing atoms that have Raman-scattered before the Ramsey readout could recover long coherence at high density.
  • The atom-number-independent instability floor indicated by $b=1.8\times10^{-18}$ suggests a technical noise source in imaging or ellipse fitting; removing it would likely push the single-clock instability below $10^{-18}$ at 1 s.
  • Because the interaction nulling near $11E_r$ already controls $\gamma_N$, applying spin squeezing in the same shallow lattice could reduce quantum projection noise without the density cost it normally brings.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript reports a systematic study of decoherence and stability in a 87Sr Wannier-Stark optical lattice clock. The authors measure lattice-depth-dependent population decay rates, extract a 3P0 clock-state lifetime of 174(28) s, and study Ramsey contrast decay as a function of dark time, atom number per site, and lattice depth. At U0=11Er and Nsite=9 they report a coherence time of about 118 s, which they argue approaches the spontaneous-emission and blackbody-radiation limit. Using imaging spectroscopy, they also report a single-clock instability of 1.5e-18 at 1 s under Tdark=7 s with 313 realizations. The paper attributes the observed decoherence to lattice Raman scattering, collisions involving spectator atoms, and density-dependent interactions, and supports the density-dependent rates with DDTWA simulations.

Significance. If the results hold, the demonstrated 118 s coherence time at a usable atom number is a major step toward spontaneous-emission-limited operation of an optical lattice clock, and the 1.5e-18 at 1 s single-region instability is a notable precision result in a shallow lattice. The paper is careful in many ways: density-dependent rates are extracted from in-situ images, the instability is a measured quantity rather than an extrapolated one, the presence of an unexplained atom-number-independent noise floor is explicitly acknowledged, and DDTWA provides an independent theoretical benchmark. The main qualification is that the 'fundamental limit' interpretation rests on a linear extrapolation in lattice depth from fits deliberately restricted to U0>50Er, applied at U0=11Er and at U0=0.

major comments (3)
  1. [Coherence time, Fig. 2(a) caption, and Abstract] The coherence time at U0=11Er and Nsite=9 is reported as 118(18) s in the body text (the paragraph following Fig. 2(a)) but as 118(9) s in the abstract and in the Figure 2(a) caption. Because this quantity is the headline result of the paper, the inconsistency must be resolved; please state which uncertainty is correct and update all occurrences consistently.
  2. [Population decay, Fig. 1 caption, Table I, and Fig. 2(d)] The lifetime 1/Γnat = 174(28) s and the Raman slope ΓR = 5.6(3)e-4 s^-1 Er^-1 used in Fig. 2(d) come from population-decay fits that the authors deliberately restrict to U0 > 50Er, while the comparison with γ0 is made at U0 = 11Er and the fundamental-limit claim involves the extrapolation to U0→0. The caption to Fig. 1 states that U0 < 50Er data are excluded to avoid complications such as Raman-scattering-induced loss and lattice intensity noise, but those same effects could introduce a nonlinear dependence of ΓL and ΓR below 50Er. The agreement of the extracted Γnat with previous lifetime measurements is reassuring but does not validate the linear model below 50Er, because the lifetime is inferred from the same extrapolated intercept. Please provide an additional test of the shallow-depth regime, for example population-decay or coherence measurements at intermediate depths such as 20-40Er, or alternatively soften the claim that the 118 s coherence time approaches the fundamental limit.
  3. [Coherence time, stretched-exponential model] The fit model C(Tdark)=C(0) exp[-(γ Tdark)^α] is used to define the coherence time as γ^-1, but the main text does not report α or C(0) for the key data points. If α differs significantly from 1, γ^-1 is not the mean decay time of the stretched exponential, so the interpretation of 'coherence time' depends on a convention that should be stated. Please report the fitted α and C(0), or explicitly define γ^-1 as the 1/e time.
minor comments (5)
  1. [Eq. (1)] The prefactor κ in the two-body loss term is not defined in the main text; please define it or refer to the supplement at the point of first use.
  2. [Fig. 2(b) and Fig. 2(e)] The nonlinearity of γ versus Nsite is accounted for by splitting the fit range, but the resulting systematic uncertainty added to γ0 and γN is not reported numerically; please state these extra uncertainties explicitly.
  3. [Fig. 2(e) and DDTWA] The text says the density-dependent decoherence is 'supported by' DDTWA but does not provide a quantitative agreement metric in the main text; please give the discrepancy or a goodness-of-fit measure, or state where in the supplement it appears.
  4. [Imaging spectroscopy, Eq. (2)] The statement that Eq. (2) is a good approximation to the classical Cramer-Rao bound 'for large atom numbers and not so small ϕ' should be made more precise; a citation to the relevant bound would help the reader judge when the approximation is valid.
  5. [Figures 1 and 2] The figure captions would be clearer if the number of independent experimental realizations per data point and the meaning of the shaded uncertainty bands (68% confidence interval of the fit versus propagated uncertainty of the model) were stated explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the coherence time and instability are directly measured, and the model bands are built from independent population-decay fits and external constants.

full rationale

The paper's headline results are measured quantities, not derived predictions: the 118(9) s coherence time is read directly from Ramsey contrast decay data (Fig. 2(a)), and the 1.5e-18/sqrt(tau) instability is a measured Allan deviation from 313 realizations of a synchronous comparison (Fig. 3(e)). The model comparison in Fig. 2(d) uses gamma_R and Gamma_nat extracted from the separate population-decay section, which is an independent observable (excited-state population loss) relative to the Ramsey coherence data; it is a consistency check, not a fit to the coherence data. The lifetime 1/Gamma_nat = 174(28) s is obtained from Gamma_L(0) minus the BBR rate, with the BBR rate taken from external references [20,27,33] and the lifetime agreeing with prior independent measurements [20,34,35]. The DDTWA simulations provide external theoretical support for the spectator-atom mechanism, and the instability comparison uses the standard QPN relation Eq. (3) with measured contrast and atom number. The extrapolation from U0 > 50 Er to U0 = 0 is a robustness concern about model applicability at shallow depths, but it is not circular: the coherence data at U0 = 11 Er are not used to construct the comparison bands, and the agreement is not enforced by construction. No self-citation chain is load-bearing for the central measured claims.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The analysis depends on a rate-equation model, an empirical stretched-exponential decay, a linear density extrapolation, and DDTWA simulations, along with several fitted decay parameters. The headline instability uses a QPN estimator whose validity conditions are stated. No new particles, forces, or mediators are introduced.

free parameters (9)
  • Gamma_e lattice-depth slope = 1.3(3)e-4 s^-1 / Er
    Linear slope from fitting population decay versus lattice depth, Table I.
  • Gamma_e offset = 2.7(4)e-2 s^-1
    Offset from the same linear fit, Table I.
  • Gamma_g = 1.2(4)e-2 s^-1
    Ground-state single-body loss rate from population decay fit, Table I.
  • Gamma_L lattice-depth slope = 4.30(7)e-4 s^-1 / Er
    Slope of e-to-g pumping rate versus lattice depth, Table I.
  • Gamma_L offset = 8.1(8)e-3 s^-1
    Zero-depth e-to-g pumping rate, used after BBR subtraction to infer the 174 s lifetime, Table I.
  • Gamma_ee = 4(1)e-6 cm^3 s^-1 K^-1
    Two-body excited-state loss coefficient from population decay fit, Table I.
  • Stretched exponential parameters C(0), gamma, alpha = Not tabulated individually
    Ramsey contrast decays are fit to C(0) exp[-(gamma*T)^alpha] for each lattice depth and density, Section Coherence time.
  • gamma0 and gammaN = Values shown in Fig. 2(d,e)
    Linear fit gamma = gamma0 + gammaN*Nsite at each lattice depth.
  • Instability floor fit a and b = experimental a=5.6e-16, b=1.8e-18; theory a=4.8e-16, b=6.5e-19
    Heuristic fit sigma_y(1s) = sqrt(a^2/N + b^2) to the atom-number dependence, Section Imaging spectroscopy.
assumptions (6)
  • domain assumption Population dynamics follow the two-species rate equation (1) with independent single-body loss, e-to-g pumping, and quadratic two-body loss.
    Used to fit Figure 1 and extract Gamma_e, Gamma_g, Gamma_L, and Gamma_ee; no derivation of the rate-equation form is given.
  • ad hoc to paper Ramsey contrast decays as a stretched exponential C(T) = C0 exp[-(gamma*T)^alpha].
    Empirical ansatz in Section Coherence time; alpha is not predicted by the physical model.
  • domain assumption gamma is linear in Nsite, gamma = gamma0 + gammaN*Nsite, and the zero-density extrapolation is unbiased.
    Used for Figure 2(b) and for extrapolating to the single-atom limit; the DDTWA is noted to be slightly nonlinear, so the authors fit two ranges.
  • domain assumption DDTWA simulations capture spectator-atom collisions and s-wave and p-wave interaction decoherence.
    The theoretical bands in Figure 2(e) rely on this approximation; details are deferred to the Supplemental Material.
  • standard math Equations (2) and (3) give the quantum projection noise limit for ellipse fitting at large atom number and not too small phase phi.
    Quoted from imaging-spectroscopy references [28,41,42] and used to estimate the theoretical QPN floor.
  • domain assumption A magic-wavelength lattice makes the trap state-independent enough that elastic Rayleigh scattering does not dephase the clock superposition.
    Standard optical-lattice-clock assumption invoked in the introduction and coherence analysis.

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Pith. "Pith review of Atomic Coherence of 2 minutes and Instability of 1.5E-18 at 1 s in a Wannier-Stark Lattice Clock." pith.science (2026). https://pith.science/paper/X7STHMM3

@misc{pith2026250506444,
  author       = {Pith},
  title        = {Pith review of: Atomic Coherence of 2 minutes and Instability of 1.5E-18 at 1 s in a Wannier-Stark Lattice Clock},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X7STHMM3}},
  note         = {Machine review of arXiv:2505.06444}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2505.06444 by the authors.

Figure 1
Figure 1. FIG. 1. Lattice depth dependent population decay rates. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Collisional interactions and the atomic coherence time. (a) Contrast of the Ramsey fringe as a function of the dark [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Estimation of atomic contribution to the clock sta [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Forward citations

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