{"id":"53ac2072-f6b5-4779-8893-62fea965d7d4","arxiv_id":"2412.02541","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A 30-atom dysprosium chain with atom-by-atom state readout shows how the collective Lamb shift varies along the chain, with drive power, and over time in Ramsey spectroscopy.","lead":"This paper reports a single-shot method to read out the internal state of every atom in an ordered 30-atom dysprosium array, and uses it to measure the collective Lamb shift in both the low-power and strong-drive regimes. The key result is a measured time-dependent frequency shift in Ramsey spectroscopy that connects the linear and nonlinear regimes and is relevant to optical clocks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unmodeled Ramsey-phase systematics (footnote 47), not mean-field, are the key risk: a pulse-area-dependent phase offset can masquerade as a 1/T frequency shift and is not excluded by a non-interacting control.","rationale":"The reader identifies the mean-field approximation as the weakest assumption, but at d=2.2λ the interaction strength is small and beyond-mean-field corrections should be negligible compared with the experimental scatter. The more load-bearing assumption is experimental: the time-dependent Ramsey shift is extracted from fringe phases, and footnote 47 admits unmodeled AOM chirp and Doppler systematics that are not in the simulations. A phase offset that depends on pulse area naturally produces a φ0/T artifact that can mimic the reported effect. The verdict remains CONDITIONAL, but the condition should be a non-interacting control and chirp calibration rather than only a beyond-mean-field test. I do not change the verdict, only the reason for it.","tokens_in":17114,"tokens_out":12061,"duration_ms":140591,"concrete_test":"Run the identical Ramsey sequence and analysis (same pulse areas θ0=π/4,π/2,3π/4 and same TRamsey range) on a non-interacting or weakly interacting configuration — e.g., a single atom or an array at d=4.5μm where δ0≈0. Extract the central-fringe shift versus TRamsey exactly as in Fig. 5(b). If any T-dependent shift of comparable magnitude appears, the central claim is not established; if the control is flat at the level of the claimed effect, the systematic concern is dismissed. As a complementary check, directly measure the AOM RF chirp during the first few hundred ns with a heterodyne or fast frequency discriminator and propagate it through the Ramsey analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is the observation of a time-dependent collective shift in Ramsey spectroscopy, Eq. (2). The data supporting it are extracted by locating the central Ramsey fringe as a function of TRamsey. Any phase offset φ0 acquired during the pulses or early in the free evolution is converted by the analysis into an apparent frequency shift φ0/TRamsey. Because φ0 can depend on pulse area — a larger θ0 accumulates more chirp during the first pulse — this artifact can reproduce the qualitative features in Fig. 5(b): a shift that depends on θ0 and evolves on the μs scale as TRamsey is varied. Footnote 47 explicitly concedes that unmodeled AOM frequency chirp and weak Doppler kicks distort the datasets and are absent from the simulations. No non-interacting control (single atom or d≫λ) is reported for the Ramsey sequence, and no independent chirp calibration is given. The mean-field approximation is less concerning here: at d=2.2λ the interaction matrix elements are only ~0.1Γ, so beyond-mean-field corrections should be second order in V/Γ and below the scatter flagged in footnote 47. The genuinely load-bearing assumption is therefore that the measured central-fringe shifts are free of an instrumentally produced 1/T tail. Without a control, the time-dependent shift central to the paper is not fully separated from this systematic.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experiment on a one-dimensional array of 30 dysprosium atoms with single-atom resolved state readout, used to study resonant dipole-dipole interactions. In the low-intensity (linear) regime, the authors measure the collective Lamb shift versus interatomic spacing, observe the single-atom excitation distribution along the chain, and show that the steady-state shift is suppressed as the drive Rabi frequency increases. In the nonlinear regime, they perform Ramsey spectroscopy and report a time-dependent collective frequency shift that interpolates between the large-excitation short-time shift and the low-excitation linear-regime shift. The central analytical result is Eq. (2), derived in a mean-field approximation, which gives the Ramsey shift as a function of the waiting time and pulse area. The appendices contain detailed mean-field derivations, simulations including positional disorder, and characterizations of the state readout.","tokens_in":17359,"tokens_out":10554,"duration_ms":104432,"significance":"If the central claims hold, the paper would provide the first single-atom-resolved measurement of the excitation distribution in an ordered array under resonant dipole-dipole interactions, and the first experimental observation of a time-dependent collective Lamb shift in Ramsey spectroscopy, with direct relevance to optical-lattice clocks. The single-shot shelving readout on a narrow intercombination transition is a notable technical achievement, and the data are made available. The derivation of Eq. (2) is parameter-free, with δ0_spectro computed from the known dipole-dipole interaction, and the mean-field simulations include thermal disorder and no fitted parameters for the prediction line. However, the central Ramsey observation is weakened by the manuscript's own admission of unmodeled systematics (footnote 47) and the absence of a non-interacting control, which leaves the time-dependent shift vulnerable to an instrumental phase-offset artifact.","major_comments":[{"comment":"The central claim of a time-dependent collective Ramsey shift is not cleanly separated from instrumental phase errors. The analysis extracts the shift from the central-fringe position; any phase offset φ0 acquired during the pulses or early free evolution is converted into an apparent frequency shift φ0/TRamsey. Since φ0 can depend on pulse area (e.g., through a frequency chirp during the pulse), this artifact can reproduce the qualitative pulse-area- and time-dependence in Fig. 5(b). Footnote 47 explicitly concedes that an AOM frequency chirp and weak Doppler kicks are present and not accounted for in the simulations. No non-interacting control (single atom or d≫λ) is reported for the Ramsey sequence, and no independent chirp calibration is given. Please provide such a control or a quantitative bound on the phase offset, or otherwise demonstrate that the observed time dependence is not of instrumental origin.","section":"§IV.B, Fig. 5, footnote 47"},{"comment":"The sign of the short-time Ramsey shift is inconsistent. The main text states that for TRamsey ≪ 1/Γ one obtains δRamsey = −δ0_spectro cosθ0 [19], but Eq. (2) evaluated in the limit T→0 gives δRamsey = +δ0_spectro cosθ0. The subsequent sentence that integrating φ̇ = −δ0_spectro cosθ(t) yields Eq. (2) is also inconsistent, since the integral of a negative rate gives a negative shift. The appendix (F) derivation, with α = ΔL − δ0 Sθ(T), leads to the positive sign. Please correct the sign in the main text and in the expression for φ̇, or explain the sign convention unambiguously.","section":"§IV.B, Eq. (2)"},{"comment":"The Ramsey data were acquired without the axial lattice, because the lattice turn-off produced systematic shifts in Ramsey interferometry (footnote 45). This also changes δ0_spectro relative to the steady-state measurements that used the lattice. Consequently, the comparison with the low-excitation shift in Fig. 5(b) is made through a simulated value for the no-lattice configuration rather than a direct measurement at the same conditions. Please state explicitly the positional disorder parameters used in the Ramsey simulations, and show how the predicted curves in Fig. 5(b) depend on them.","section":"§IV.B, footnote 45"}],"minor_comments":[{"comment":"The word 'frive' in 'increasing the frive Rabi frequency' should read 'drive'.","section":"§IV.A"},{"comment":"The symbol θ0 is used both for the pulse area and for the Bloch angle; please define the connection clearly to avoid confusion between the initial pulse area and the time-varying angle θ(t).","section":"§IV.B"},{"comment":"The statement that the probe beam has 'mostly σ− and σ+ polarization components' should be reconciled with the earlier description of the drive as σ−; please clarify how the two-level isolation is maintained in the Ramsey measurements given the additional σ+ component.","section":"§IV.B, footnote 46"},{"comment":"The dashed-dotted orange line is described as the predicted δ0_spectro shift calculated in the low-intensity regime; it would be helpful to quote the numerical value and its uncertainty in the caption, rather than only referring to the figure.","section":"Fig. 5(b) caption"}],"recommendation":"major_revision","confidential_remarks":"The steady-state results (Figs. 2–4) appear solid and are a valuable contribution in themselves. The Ramsey part is the most novel claim, but the absence of a non-interacting control combined with the manuscript's own admission of unmodeled AOM chirp and Doppler shifts makes the time-dependent shift insufficiently supported. The sign inconsistency in the main text around Eq. (2) is a separate but easily fixed issue. I recommend major revision rather than rejection, because the central derivation is sound and the required control or calibration is within the scope of the present experimental platform."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis paper is worth your time. What is actually new: the authors measure the collective Lamb shift in a 30-atom 1D array both in the low-intensity steady-state regime and in Ramsey spectroscopy, and they observe the Ramsey shift evolving as the excited state decays. That time dependence connects the large-excitation shift to the linear-regime shift and, as far as I know, has not been seen before. They also demonstrate single-atom-resolved single-shot state readout on the narrow intercombination transition and use it to map the excitation profile along the chain. The readout is a genuinely useful technical step.\n\nThe paper is careful. The mean-field derivations in Appendices E and F are explicit, Eq. (2) is a clean extension of the short-time result, and the authors credit the earlier theory (Chang, Ye, Lukin; Cidrim et al.) properly. The steady-state shift suppression with drive power in Fig. 4 is a good consistency check. The data analysis includes calibrations for detection errors and site-dependent survival, and the data are publicly available.\n\nThe soft spots are real but manageable. The Ramsey data were taken without the axial lattice (footnote 45), and footnote 47 concedes unmodeled AOM chirp and weak Doppler kicks. A constant phase offset in the Ramsey sequence would indeed show up as a 1/T frequency shift in the analysis. But the data argue against that being the dominant effect: the π/2 and 3π/4 shifts rise with TRamsey, which is the opposite of a 1/T artifact, and the π/4 data are nearly flat, which would be very sensitive to such a term. So the central claim holds up, though a non-interacting control would have made it airtight. The mean-field approximation is the main theoretical limitation, but at d=2.2λ the interaction matrix elements are about 0.1Γ, so beyond-mean-field corrections should be small; the authors say as much and point to shorter spacings as the place to look.\n\nMy recommendation: send this to peer review. It is a serious experimental paper with a new result and an honest discussion of its own limitations. Ask the authors for a non-interacting control or at least a quantitative bound on the chirp, and to address footnote 47 more systematically, but do not desk reject it.","headline":"First observation of a time-dependent collective Lamb shift in a 1D atomic array, with a new single-atom readout; the main claim survives the systematic-error concern, but a non-interacting control would have made it airtight.","tokens_in":17929,"tokens_out":3841,"would_cite":true,"duration_ms":36158,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Collective frequency shifts in a 30-atom chain evolve during Ramsey spectroscopy, linking strong-pulse behavior to the low-excitation collective Lamb shift.","keywords":["collective Lamb shift","Ramsey spectroscopy","one-dimensional atomic array","resonant dipole-dipole interactions","mean-field approximation","single-atom resolved readout","dysprosium optical tweezers","optical lattice clock shifts"],"falsifier":"Measure the Ramsey shift on the same array at a shorter spacing, e.g. $d = 2\\lambda$ (1.25 $\\mu$m), where the paper itself expects beyond-mean-field effects, and compare the full curve of $\\delta_{\\rm Ramsey}$ versus $T_{\\rm Ramsey}$ to the central formula; a systematic departure that grows with pulse area and density would show the mean-field integration is incomplete. A more direct test would be to measure the two-atom correlation function during the wait time and check whether it stays factorizable as the mean-field approximation requires.","tokens_in":16900,"feed_emoji":"⚛️","tokens_out":6621,"duration_ms":62737,"temperature":0.7,"pith_summary":"The paper uses a 30-atom one-dimensional dysprosium array with single-atom state readout to watch how cooperative resonant dipole-dipole interactions shift the atomic transition. In low-intensity steady-state spectroscopy it measures the collective Lamb shift versus interatomic spacing, and it observes how excitation builds up along the chain atom by atom. In Ramsey spectroscopy, with pulse areas up to 3π/4 and wait times comparable to the excited-state lifetime, it finds that the shift of the central fringe changes with the free-evolution time. The paper's central result is an analytical mean-field formula for this time-dependent Ramsey shift that connects the strong-pulse regime to the familiar low-excitation collective shift. If correct, it gives a direct physical handle on density-dependent frequency shifts in ordered optical-lattice clocks.","feed_headline":"Collective Lamb shift evolves during Ramsey spectroscopy","feed_subtitle":"Ramsey fringes on a 30-atom dysprosium chain show a frequency shift that evolves in time toward the low-excitation collective Lamb shift.","key_machinery":"The load-bearing mechanism is the instantaneous precession rate of each atomic Bloch vector in the field radiated by the other atoms. In a mean-field treatment truncated at first order in the dipole-dipole couplings, the rate is $\\dot{\\phi}(t) = -\\delta^0_{\\rm spectro}\\cos\\theta(t)$, with $\\theta(t)$ the instantaneous excitation angle set by spontaneous decay. Averaging this rate over the Ramsey wait time gives the central formula; this integration of the time-dependent precession, rather than a static line shift, is what carries the argument. The supporting machinery is the single-shot shelving readout on the broad 421 nm line, which projects each atom's internal state and reveals the per-site excitation pattern.","core_discovery":"The central discovery is that the collective frequency shift seen in Ramsey spectroscopy on a 30-atom one-dimensional array is not constant but evolves during the wait time between the two pulses, and that its evolution is captured by $\\delta_{\\rm Ramsey} = \\delta^0_{\\rm spectro}\\left[1 - \\frac{(1 - e^{-\\Gamma T_{\\rm Ramsey}})(1-\\cos\\theta_0)}{\\Gamma T_{\\rm Ramsey}}\\right]$. Here $\\delta^0_{\\rm spectro}$ is the low-excitation, linear-regime spectroscopic shift, $\\Gamma$ the excited-state linewidth, $T_{\\rm Ramsey}$ the free-evolution time, and $\\theta_0$ the first pulse area. The formula interpolates between $\\delta_{\\rm Ramsey} = -\\delta^0_{\\rm spectro}\\cos\\theta_0$ at short times and $\\delta^0_{\\rm spectro}$ at long times, so the shift measured in a Ramsey clock naturally converges to the linear-optics collective Lamb shift as the excited-state population decays. Single-atom-resolved readout is what makes the comparison direct: the excitation distribution along the chain is measured per atom, not inferred from scattered light. The authors treat this as establishing, experimentally, a connection between the large-excitation and low-excitation regimes of the collective Lamb shift.","pith_inferences":["Because the central formula is derived to first order in the interactions, one can use it as a quantitative benchmark by pushing to shorter spacings or larger arrays, where beyond-mean-field correlations are expected; deviations would define where the mean-field picture breaks down.","The per-atom excitation gradient measured along the chain could serve as a local field-strength meter, extending this technique to diagnose cooperative scattering in other geometries such as two-dimensional arrays.","With repumping restored, the readout is lossless in principle and could enable repeated interrogation cycles, allowing measurements of correlations between successive Ramsey shots and direct tests of factorizability at the two-atom level."],"forward_implications":["In an optical-lattice clock operating with Ramsey interrogation, the density-dependent clock shift is not simply a constant offset; its value during the interrogation depends on pulse area and wait time, and it approaches the low-excitation shift once the excited-state population has decayed.","The same single-atom-resolved readout can map how resonant dipole-dipole interactions redistribute excitation along a chain, showing the effective focusing of the drive as the field propagates through the array.","At fixed spacing, increasing the drive Rabi frequency suppresses the steady-state collective shift approximately as $1/(1 + 2\\Omega^2/\\Gamma^2)$, because the average atomic dipole shrinks as the drive strengthens.","The measured time-dependent Ramsey shift agrees with mean-field master-equation simulations, supporting the use of such treatments for ordered arrays at spacings around $2.2\\lambda$ in the regime studied."],"supporting_citations":[{"why":"Supplies the short-time Ramsey-shift formula and the cos(theta0) dependence that the paper's time-dependent formula generalizes.","marker":"[19]"},{"why":"Provides the prior one-dimensional-array collective shift measurement and the mean-field simulation method used for comparison.","marker":"[10]"},{"why":"The optical-clock experiment whose pulse-area-dependent cooperative shift is connected to the present time-dependent measurement.","marker":"[21]"},{"why":"Theoretical treatment of dipole-dipole frequency shifts at longer times and in multilevel atoms, extended here to a two-level one-dimensional setting.","marker":"[20]"},{"why":"Predicts position-dependent excitation along an array; the paper's single-atom readout confirms this prediction.","marker":"[39]"},{"why":"Earlier cooperative Lamb shift measurement in a mesoscopic array, used as a baseline for the low-excitation steady-state shift.","marker":"[5]"},{"why":"Atom-by-atom rearrangement method used to prepare the defect-free 30-atom chain.","marker":"[32]"}],"fun_headline_variants":["Collective Lamb shift evolves during Ramsey spectroscopy","Ramsey fringes expose time-varying collective shift","Single-atom readout shows Lamb shift changing in time","30-atom chain reveals dynamic collective Lamb shift","Large-excitation shift converges to linear-regime value"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central assumption is that a mean-field description, in which each atom feels only the average field of the others and quantum correlations are neglected, is accurate for 30 atoms spaced by about 2.2 wavelengths; the analytical formula and all simulated curves inherit this assumption.","fun_headline_variants_meta":{"raw":{"variants":["Collective Lamb shift evolves during Ramsey spectroscopy","Ramsey fringes expose time-varying collective shift","Single-atom readout shows Lamb shift changing in time","30-atom chain reveals dynamic collective Lamb shift","Large-excitation shift converges to linear-regime value"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000687,"raw_usage":{"total_tokens":3175,"prompt_tokens":1067,"completion_tokens":2108,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":2035}},"tokens_in":683,"tokens_out":2108,"duration_ms":15395,"temperature":1.0,"reasoning_tokens":2035,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:20:19.707034+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the Ramsey shift on the same array at a shorter spacing, e.g. $d = 2\\lambda$ (1.25 $\\mu$m), where the paper itself expects beyond-mean-field effects, and compare the full curve of $\\delta_{\\rm Ramsey}$ versus $T_{\\rm Ramsey}$ to the central formula; a systematic departure that grows with pulse area and density would show the mean-field integration is incomplete. A more direct test would be to measure the two-atom correlation function during the wait time and check whether it stays factorizable as the mean-field approximation requires.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the short-time Ramsey-shift formula and the cos(theta0) dependence that the paper's time-dependent formula generalizes."},{"cited_title":"Glicenstein, G","cited_arxiv_id":null,"evidence_quote":"Provides the prior one-dimensional-array collective shift measurement and the mean-field simulation method used for comparison."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The optical-clock experiment whose pulse-area-dependent cooperative shift is connected to the present time-dependent measurement."},{"cited_title":"Cidrim, A","cited_arxiv_id":null,"evidence_quote":"Theoretical treatment of dipole-dipole frequency shifts at longer times and in multilevel atoms, extended here to a two-level one-dimensional setting."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicts position-dependent excitation along an array; the paper's single-atom readout confirms this prediction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier cooperative Lamb shift measurement in a mesoscopic array, used as a baseline for the low-excitation steady-state shift."},{"cited_title":"Endres, H","cited_arxiv_id":null,"evidence_quote":"Atom-by-atom rearrangement method used to prepare the defect-free 30-atom chain."}],"review_version":1}