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REVIEW 4 major objections 6 minor 61 references

Measurement and control of the interaction frequency shift in bosonic optical lattice clocks

T0 review · 4 major / 6 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read The paper shows that the density shift in a 88Sr bosonic optical lattice clock is a nonlinear effect that can be cancelled at a specific clock detuning, and reports the first measurement of the inter-level scattering length a_eg.

desk verdict Solid experimental work on bosonic clock shifts, but the factor-of-2 disagreement between two ways of extracting U_eg needs reconciliation before I'd trust the quantitative claims. read the letter →

arxiv 2608.02425 v1 pith:MT3CCFSG submitted 2026-08-03 physics.atom-ph quant-ph

J. P. Salvatierra , M. Barbiero , G. Bertaina , D. Calonico , F. Levi , M. G. Tarallo This is my paper · ORCID
classification physics.atom-phquant-ph
keywords opticallatticeclocks88Srbosonicatomsdensity-dependentshiftinteractionsidebandcollectivespinmodeldephasingscatteringlength
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

The paper establishes that the interaction-induced frequency shift in a 88Sr bosonic optical lattice clock is not simply proportional to density: it is a nonlinear function of the per-site occupation number, with a sign that can reverse. The authors show that a collective spin Hamiltonian plus a density-dependent dephasing channel reproduces both the Rabi line shapes and the measured shift curves, and that by locking the clock at a specific detuning (δ_lock/Ω ≈ 0.94 in a 2D lattice, 1.4 in 1D) the net density shift can be cancelled. This makes bosonic clocks viable for precision metrology and yields a first reported value for the inter-level scattering length a_eg = -125(12) a0.

What carries the argument

The central object is the collective spin Hamiltonian H = -ℏδS_z - ℏΩS_x + C(N-1)S_z + χS_z^2, where S are collective spin operators for the two clock states and C, χ encode linear and nonlinear interaction energies. To match the 1D data, the model must be complemented by a dissipative mean-field optical Bloch equation with a density-dependent dephasing rate γ_deph, derived from second-order radial fluctuations. This machinery connects the microscopic scattering lengths to the observed line shapes and clock shifts.

What would settle it

Measure the 1D clock shift at high atom numbers with a lattice depth scan: the model predicts a specific sign change and magnitude tied to κ^(2)_eg; if the shift keeps growing linearly or shows a different zero-crossing, the assumed dephasing channel or the κ^(2)_eg = 1 choice fails. Alternatively, directly probe the e–g coherence lifetime via spin-echo Ramsey spectroscopy at high density; if the coherence survives longer than the collision correlation time, the justification for κ^(2)_eg = 1 collapses.

Watch

Extended reading notes

Core claim

In a 88Sr optical lattice clock, the clock transition frequency shift induced by atom-atom interactions grows nonlinearly with the number of atoms per lattice site. In a 2D lattice, the Rabi spectrum shows a resolved interaction sideband consistent with the collective spin model (Eq. 1), while in a 1D lattice the shift is reproduced only when a density-dependent dephasing channel (γ_deph ≈ 1.3 s^-1) is included in the mean-field Bloch equations. Fitting the shift versus atom number and versus lock detuning gives interaction energies U_eg/h = -15(2) Hz (2D), U_ee/h = 12(4) Hz, and U_eg/h = -0.14(4) Hz, U_ee/h = 0.25(3) Hz (1D). From these, the authors derive the first measured inter-level sca

Load-bearing premise

The whole analysis leans on an effective spin model that assumes the radial motion decouples from the spin dynamics (Born factorization) and that all density-dependent decoherence can be captured by a single fitted dephasing rate; in the 1D case the fit also requires assuming the e–g thermal bunching factor κ^(2)_eg equals 1 rather than the ideal thermal value 2.

Editorial extensions

If this is right

  • Bosonic 88Sr lattice clocks can be operated at a 'magic' detuning and density where the collisional shift is cancelled, removing the main barrier to high accuracy for bosonic clocks.
  • The measured a_eg and a_ee provide benchmarks for ab initio calculations of the Sr 1S0–3P0 potential and for photoassociation spectroscopy.
  • The collective spin description applies to thermal (non-degenerate) ensembles, not just quantum degenerate gases.
  • The extracted interaction parameters open the way to realizing an XXZ spin model and adiabatic spin squeezing protocols in bosonic lattices.
  • Precision isotope shift measurements on bosonic Sr isotopes, used for new-physics searches, can be corrected for interaction shifts.

Reading between the lines

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

  • The cancellation mechanism at δ_lock/Ω ≈ 0.94 is not limited to Sr: any bosonic clock with s-wave interactions and a similar spin model should exhibit a detuning-dependent zero-crossing, which could be tested in other species.
  • If κ^(2)_eg = 1 reflects genuine e–g coherence collapse on collision timescales, then reducing radial thermal fluctuations (colder temperatures or deeper lattices) should bring the 1D shift closer to the unitary prediction; a scan of U_0 versus shift would test this.
  • The first a_eg = -125 a0 can be cross-checked by clock-line photoassociation in a lattice, which would measure the e–g interaction potential directly.
  • The sign reversal of the shift with N_tot suggests that at higher occupancy, the clock frequency may be density-insensitive in a plateau region; optimizing operation there could reduce sensitivity to atom-number fluctuations.
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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

4 major / 6 minor

Summary. The paper reports measurements of the interaction-induced clock shift in a bosonic 88Sr optical lattice clock in both 1D and 2D lattice geometries. The central claims are: (i) the density shift becomes nonlinear in the per-site occupation number even for thermal atoms; (ii) in a 2D lattice the Rabi lineshape exhibits an interaction sideband consistent with a collective spin model, and in 1D the shift is modified by density-induced dephasing; (iii) by choosing the clock locking detuning relative to the Rabi frequency, the interaction shift can be cancelled, enabling operation at a net-zero systematic density shift. From fits, the authors extract U_eg/h = -15(2) Hz and U_ee/h = 12(4) Hz in 2D, and U_eg/h = -0.14(4) Hz and U_ee/h = 0.25(3) Hz in 1D, and derive the first reported e-g scattering length a_eg = -125(12) a0. The paper also projects the model toward many-body physics and isotope-shift metrology.

Significance. If the quantitative results hold, this is a significant advance for bosonic optical lattice clocks: it demonstrates that the interaction shift is not simply linear in density, that a collective-spin description captures the measured lineshape and frequency shifts, and that a magic-density operating point can be reached in principle. The deduced a_eg would be the first experimental value for the 1S0-3P0 scattering length in 88Sr and would provide a benchmark for theory and photoassociation. The work also connects to ongoing efforts to use bosonic clocks in isotope-shift searches for new physics. The paper is generally careful in its measurement methodology, with interleaved comparisons, explicit statistical uncertainties, and a detailed Supplemental Material that includes a microscopic derivation of the effective spin model. However, the central quantitative claims—the value of U_eg, the derived scattering length, and the predicted cancellation points—rest on a model-dependent analysis that currently contains an unresolved factor-of-two ambiguity, as detailed below. The qualitative observation of a nonlinear, sign-reversing density shift appears robust, but the specific quantitative

major comments (4)
  1. [Results, Fig. 1(c) and Fig. 2; Table I] The same 2D dataset yields two inconsistent values of U_eg/h: the heuristic sideband model gives -32(8) Hz (Fig. 1c), while the collective spin-model fit to the locking-point and N_tot data gives -15(2) Hz (Fig. 2). The paper does not explain why one value is preferred or how the two analyses are reconciled. Table I adopts the spin-model value, and the derived a_eg = -125(12) a0 and the cancellation condition δ_lock/Ω = 0.94(3) depend directly on this choice. Since the two values differ by a factor of two, the claimed scattering length and magic-density point are not uniquely determined. The authors should either provide a simultaneous description of the sideband and the density-shift data with a single U_eg, or report the discrepancy as a systematic uncertainty and explain its origin.
  2. [Supplemental Material, 'Spin model of interacting bosons in an optical lattice'] In the 1D analysis, the correlation coefficient κ^(2)_eg is set to 1 instead of the ideal-thermal-boson value 2, with only the phrase 'collapse of the e-g coherence' as justification. This rescales U_eg by a factor of two in the 1D channel and is not independently verified by any measurement or derivation in the manuscript. The same factor-of-two ambiguity appears in the 2D sideband-versus-spin-model discrepancy, suggesting a common systematic issue. Because U_eg is the key parameter that determines both the sign-reversal behavior and the magic-density condition, the fit cannot be considered a unique determination unless κ^(2)_eg is measured or derived from a concrete microscopic model, or the fit is repeated with κ^(2)_eg as a free parameter with a prior that reflects the theoretical uncertainty.
  3. [Supplemental Material, first paragraph; Eqs. (S.27)-(S.29)] The microscopic derivation of the dissipative spin model is deferred to the authors' own paper, Ref. [56], which is listed as 'in preparation'. The Supplemental Material provides a sketch, but the second-order Born-Markov dephasing channel of Eq. (S.28) and the conditions under which it reduces to the phenomenological γ_deph term are not fully derived here. Since this dephasing channel is load-bearing for the 1D fits and for the claimed breakdown of the unitary model, the manuscript should either include the full derivation or clearly state that the model is phenomenological. Relying on an unpublished reference for a central part of the analysis is not sufficient support for the quantitative claims.
  4. [Results, Figs. 2 and 3; Conclusions] The claimed cancellation of the interaction shift at δ_lock/Ω = 0.94(3) (2D) and 1.4 (1D) is an extrapolation from the fitted curves, not a direct measurement at the predicted zero. In the 1D case, the inset of Fig. 3 shows data consistent with the predicted trend but with uncertainties comparable to the expected shift; no direct zero-crossing verification is presented. Given that the cancellation point is a central practical claim, the authors should either provide a direct interleaved measurement at the predicted condition or explicitly state that the zero is a model-dependent prediction and quantify how the parameter uncertainty (including the factor-of-two ambiguity) propagates to the net-zero condition.
minor comments (6)
  1. [Fig. 1 caption] Typo: 'gtoeinterrogation' should read 'g-to-e interrogation'.
  2. [Main text, after Eq. (1)] The occupation distribution is written as 'mR(m)' but R(m) is described as a probability. Use P(m) or another symbol to avoid confusion with the Rabi frequency Ω.
  3. [Eq. (3) and Supplemental Material] The dephasing term in Eq. (3) contains (N-1)(1-w)u, which is not obviously the mean-field limit of Eq. (S.28) because the latter is expressed in terms of ρ_ee and ρ_gg. The connection should be made explicit in the main text or by a cross-reference.
  4. [Table I] The sign convention for U_eg/h in 1D and 2D is not stated in the table caption. The reader must infer the sign from the text; please add a note.
  5. [Figure 3, dashed lines] The explanation that the unitary prediction doubles U_eg to account for κ^(2)_eg = 1 is clear in words but the figure legend should state this explicitly, since otherwise the dashed and solid lines appear to use different parameters.
  6. [References] Reference [29] is to 'Supplemental Material at [URL]'; in a published version, this should be replaced by a permanent link or a proper citation to the supplementary material.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction found; core results are data-driven fits, with a minor unverified modeling assumption and an unreconciled internal inconsistency noted.

full rationale

The paper's central quantitative claims are obtained by fitting the collective spin model (Eq. 1) and dissipative mean-field equations (Eqs. 3) to measured frequency shifts, then converting the fitted interaction energies into scattering lengths via the thermally-averaged relation in Eq. (S.18). This is ordinary parameter extraction, not circular: the fitted U_eg and U_ee are not defined in terms of the claimed 'magic' cancellation points; rather, the cancellation points are zero crossings of the fitted model. The inset of Fig. 3 compares data at fixed N_tot with curves computed from parameters fitted to the N_tot-dependence; this is a global-fit consistency check, and the text does not claim an independent prediction from it. The 1D κ^(2)_eg = 1 assumption, introduced in the Supplemental Material ('we have tested the case κ^(2)_eg,µ ≃ 1') and used to reconcile 1D and 2D data, is an unverified modeling choice; similarly, the factor-of-two disagreement between the heuristic sideband extraction (U_eg/h = -32(8) Hz) and the spin-model fit (-15(2) Hz) is an unreconciled internal inconsistency that affects the derived a_eg. These are correctness risks, not circular reductions, because the assumptions are not imposed by requiring the target result a_eg. The paper also states 'A full derivation will be presented elsewhere [56]', a self-citation to an in-preparation work; the Supplemental Material provides the derivation skeleton and the spin model is attributed to the independent Ref. [11], so this self-citation is not load-bearing. Overall, no step in the derivation reduces to its own inputs by construction.

Assumptions & free parameters 8 free parameters · 7 assumptions · 1 invented entities

The analysis rests on a chain of modeling assumptions that convert measured Rabi lineshapes and interleaved frequency shifts into interaction energies and scattering lengths: thermal radial states with Born factorization, negligible tunneling, mean-field closure, and a fitted density-dependent dephasing channel. The paper supplies a partial microscopic derivation in the Supplement but explicitly defers the 'full derivation' to the authors' own in-preparation paper [56], and several free parameters (U_eg, U_ee, γ_deph, offsets, and the κ^(2)_eg adjustment) are fitted to the same data used to infer the magic cancellation. No new physical entities are introduced except a formal vacancy state for losses.

free parameters (8)
  • U_eg/h (2D lattice) = -15(2) Hz
    Fitted from simultaneous spin-model fit of Rabi shift vs N_tot and δ_lock; drives the negative shift and cancellation point.
  • U_ee/h (2D lattice) = 12(4) Hz
    Fitted from same 2D data; positive nonlinear interaction term.
  • U_eg/h (1D lattice) = -0.14(4) Hz
    Fitted from 1D density-shift measurements at three lock detunings.
  • U_ee/h (1D lattice) = 0.25(3) Hz
    Fitted from 1D density-shift measurements.
  • γ_deph (1D dephasing rate) = 1.3(2) s^-1, or γ_deph/n0 = 120(20) µm^3/s
    Fitted dissipative mean-field parameter; 2D fit is consistent with zero.
  • Absolute frequency offsets = 0.16(4) Hz and 0.16(12) Hz
    Fitted offsets pinning the absolute shift at the reference atom number in the 2D and 1D datasets.
  • κ^(2)_eg correlation coefficient (1D) = 1
    Ad hoc reduction from ideal-thermal-boson value 2 to 1 in the 1D analysis to reconcile dephasing; no independent measurement.
  • β_ee two-body loss coefficient = 21(7) µm^3/s (1D), 10.0(15) µm^3/s (2D)
    Fitted from excited-state decay curves; used as a consistency check on single-atom density/volume.
assumptions (7)
  • domain assumption Negligible tunneling between lattice wells and longitudinal freezing to a single orbital.
    Invoked in Theory section before Eq. (1) and in Supplement Eq. (S.2); required for the independent-well spin model.
  • domain assumption Born factorization ρ(t) ≈ ρ_s(t) ⊗ ρ_th_r and diagonal thermal radial state.
    Supplement assumptions (v)-(vi), Eq. (S.10); required for radial elimination and the effective spin Hamiltonian.
  • domain assumption Short-lived, pair-local radial correlations leading to a Markovian Lindblad dephasing channel of the form γ_deph Σ D[P_e^(i) s_z^(j)].
    Supplement Eqs. (S.27)-(S.28); the functional form of the fitted dephasing is assumed, not measured independently.
  • ad hoc to paper Ideal thermal bosonic radial modes have bunching factor g^(2)=2 for all spin combinations; later revised to κ^(2)_eg=1 in 1D.
    Supplement Eq. (S.15) and Results 1D paragraph; the 1D revision is introduced to make the model fit and is not independently verified.
  • domain assumption Mean-field factorization of quadratic spin correlators: ⟨S_α S_β + S_β S_α⟩ ≈ 2⟨S_α⟩⟨S_β⟩.
    Used in the mean-field optical Bloch equations, Eq. (S.43); neglects quantum correlations in the dissipative model.
  • domain assumption Gaussian harmonic-oscillator Wannier functions and thermal occupations for the volume integrals.
    Supplement Eqs. (S.18)-(S.20); the absolute density/volume calibration determines U_ij and the derived scattering lengths.
  • domain assumption Two-body loss channels can be represented by a single local vacancy state per site in the reduced spin model.
    Supplement Eqs. (S.30)-(S.31); simplifies losses but assumes all loss products are untrapped and irrelevant to spin dynamics.
invented entities (1)
  • Vacancy state |0⟩ per lattice site in the local-spin loss model
    purpose: Represents all two-body loss product channels in the reduced spin model; allows pair-removal jumps to be written as local Lindblad operators.
    A bookkeeping sink state, not a physical new species; no external falsifiable handle, but also not an ontological claim.

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Pith. "Pith review of Measurement and control of the interaction frequency shift in bosonic optical lattice clocks." pith.science (2026). https://pith.science/paper/MT3CCFSG

@misc{pith2026260802425,
  author       = {Pith},
  title        = {Pith review of: Measurement and control of the interaction frequency shift in bosonic optical lattice clocks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MT3CCFSG}},
  note         = {Machine review of arXiv:2608.02425}
}
abstract

We report precise measurements of inter-level interactions in a bosonic optical lattice clock based on $^{88}$Sr atoms. We observe a nonlinear density dependence of the clock shift, even without reaching quantum degeneracy. In a 2D lattice, the Rabi line shape exhibits an interaction sideband consistent with a collective spin model, while in a 1D lattice the shift is modified by density-induced dephasing. These findings, combined with a careful choice of interrogation detuning and atomic density, can enable operation at a net-zero systematic density shift in $^{88}$Sr lattice clocks. We discuss the implications of these findings in many-body physics, quantum simulation, and precision isotope shift measurements, which provide a powerful probe for new physics beyond the Standard Model.

Figures

Figures reproduced from arXiv: 2608.02425 by the authors.

Figure 1
Figure 1. FIG. 1. Rabi spectroscopy of interacting bosons in optical lattices. a) Fraction of the atomic population contributing to [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Observation of clock frequency shift in a 2D lattice [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. These lineshapes were obtained by scanning the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: FIG. 3. Measurement of the interaction frequency shift in a [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]

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Works this paper leans on

61 extracted references · 2 canonical work pages

  1. [56]

    Bertaina, J

    G. Bertaina, J. P. Salvatierra, and M. G. Tarallo (2026), in preparation

    2026

  2. [1]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Optical atomic clocks, Rev. Mod. Phys.87, 637 (2015)

    2015

  3. [2]

    Derevianko and H

    A. Derevianko and H. Katori, Colloquium: Physics of optical lattice clocks, Reviews of Modern Physics83, 331 (2011)

    2011

  4. [3]

    W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Sch¨ affer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Mi- lani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, Atomic clock performance enabling geodesy below the centimetre level, Nature564, 87 (2018)

    2018

  5. [4]

    Bothwell, C

    T. Bothwell, C. J. Kennedy, A. Aeppli, D. Kedar, J. M. Robinson, E. Oelker, A. Staron, and J. Ye, Resolving 6 the gravitational redshift across a millimetre-scale atomic sample, Nature602, 420 (2022)

    2022

  6. [5]

    Aeppli, K

    A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Clock with 8×10−19 systematic uncertainty, Phys- ical Review Letters133, 10.1103/physrevlett.133.023401 (2024)

    doi:10.1103/physrevlett.133.023401 2024

  7. [6]

    Filzinger, S

    M. Filzinger, S. D¨ orscher, R. Lange, J. Klose, M. Steinel, E. Benkler, E. Peik, C. Lisdat, and N. Huntemann, Improved limits on the coupling of ultralight bosonic dark matter to photons from optical atomic clock com- parisons, Physical Review Letters130, 10.1103/phys- revlett.130.253001 (2023)

    doi:10.1103/phys- 2023

  8. [7]

    M. S. Safronova, The search for variation of funda- mental constants with clocks, Annalen der Physik531, 10.1002/andp.201800364 (2019)

    work page doi:10.1002/andp.201800364 2019

Show all 61 references
  1. [8]

    Sherrill, A

    N. Sherrill, A. O. Parsons, C. F. A. Baynham, W. Bow- den, E. Anne Curtis, R. Hendricks, I. R. Hill, R. Hobson, H. S. Margolis, B. I. Robertson, M. Schioppo, K. Szy- maniec, A. Tofful, J. Tunesi, R. M. Godun, and X. Cal- met, Analysis of atomic-clock data to constrain varia- t...

    2023

  2. [9]

    Shinkai, M

    H. Shinkai, M. Takamoto, and H. Katori, Transportable optical lattice clocks and general relativity, Interna- tional Journal of Modern Physics D34, 2540012 (2025), https://doi.org/10.1142/S0218271825400127

    2025 doi

  3. [10]

    Riehle, Towards a redefinition of the second based on optical atomic clocks, Comptes Rendus Physique16, 506 (2015), the measurement of time / La mesure du temps

    F. Riehle, Towards a redefinition of the second based on optical atomic clocks, Comptes Rendus Physique16, 506 (2015), the measurement of time / La mesure du temps

    2015

  4. [11]

    A. Rey, A. Gorshkov, C. Kraus, M. Martin, M. Bishof, M. Swallows, X. Zhang, C. Benko, J. Ye, N. Lemke, and A. Ludlow, Probing many-body interactions in an optical lattice clock, Annals of Physics340, 311 (2014)

    2014

  5. [12]

    Aeppli, A

    A. Aeppli, A. Chu, T. Bothwell, C. J. Kennedy, D. Kedar, P. He, A. M. Rey, and J. Ye, Hamiltonian engineer- ing of spin-orbit–coupled fermions in a wannier-stark optical lattice clock, Science Advances8, 10.1126/sci- adv.adc9242 (2022)

    2022 doi

  6. [13]

    J. C. Berengut, D. Budker, C. Delaunay, V. V. Flam- baum, C. Frugiuele, E. Fuchs, C. Grojean, R. Harnik, R. Ozeri, G. Perez, and Y. Soreq, Probing new long- range interactions by isotope shift spectroscopy, Phys. Rev. Lett.120, 091801 (2018)

    2018

  7. [14]

    K. Ono, Y. Saito, T. Ishiyama, T. Higomoto, T. Takano, Y. Takasu, Y. Yamamoto, M. Tanaka, and Y. Takahashi, Observation of nonlinearity of generalized king plot in the search for new boson, Phys. Rev. X12, 021033 (2022)

    2022

  8. [15]

    J. C. Berengut and C. Delaunay, Precision isotope-shift spectroscopy for new physics searches and nuclear in- sights, Nature Reviews Physics7, 119 (2025)

    2025

  9. [16]

    Zelevinsky, M

    T. Zelevinsky, M. M. Boyd, A. D. Ludlow, T. Ido, J. Ye, R. Ciury lo, P. Naidon, and P. S. Julienne, Narrow line photoassociation in an optical lattice, Physical Review Letters96, 203201 (2006)

    2006

  10. [17]

    Akatsuka, M

    T. Akatsuka, M. Takamoto, and H. Katori, Optical lat- tice clocks with non-interacting bosons and fermions, Na- ture Physics4, 954 (2008)

    2008

  11. [18]

    Lisdat, J

    C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, Collisional losses, decoherence, and fre- quency shifts in optical lattice clocks with bosons, Phys- ical Review Letters103, 090801 (2009)

    2009

  12. [19]

    Takano, R

    T. Takano, R. Mizushima, and H. Katori, Precise deter- mination of the isotope shift of88sr–87sr optical lattice clock by sharing perturbations, Applied Physics Express 10, 072801 (2017)

    2017

  13. [20]

    Origlia, M

    S. Origlia, M. S. Pramod, S. Schiller, Y. Singh, K. Bongs, R. Schwarz, A. Al-Masoudi, S. D¨ orscher, S. Herbers, S. H¨ afner, U. Sterr, and C. Lisdat, Towards an optical clock for space: Compact, high-performance optical lat- tice clock based on bosonic atoms, Physical Review ...

    2018

  14. [21]

    T. C. Killian, D. G. Fried, L. Willmann, D. Landhuis, S. C. Moss, T. J. Greytak, and D. Kleppner, Cold col- lision frequency shift of the1s-2stransition in hydrogen, Physical Review Letters81, 3807 (1998)

    1998

  15. [22]

    D. M. Harber, H. J. Lewandowski, J. M. McGuirk, and E. A. Cornell, Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas, Phys. Rev. A66, 053616 (2002)

    2002

  16. [23]

    J. S. R. Vellore Winfred,Investigation of collisional losses and decoherence in a 1-D optical lattice clock with 88Sr, phdthesis, Gottfried Wilhelm Leibniz Universit¨ at Han- nover (2010)

    2010

  17. [24]

    Bonnin, C

    A. Bonnin, C. Solaro, X. Alauze, and F. Pereira dos San- tos, Magic density in a self-rephasing ensemble of trapped ultracold atoms, Phys. Rev. A99, 023627 (2019)

    2019

  18. [25]

    Bloch, Ultracold quantum gases in optical lattices, Na- ture Physics1, 23 (2005)

    I. Bloch, Ultracold quantum gases in optical lattices, Na- ture Physics1, 23 (2005)

    2005

  19. [26]

    Katori, T

    H. Katori, T. Ido, and M. Kuwata-Gonokami, Opti- mal design of dipole potentials for efficient loading of sr atoms, Journal of the Physical Society of Japan68, 2479 (1999)

    1999

  20. [27]

    R. H. Dicke, The effect of collisions upon the doppler width of spectral lines, Physical Review89, 472 (1953)

    1953

  21. [28]

    Lhuillier and F

    C. Lhuillier and F. Lalo¨ e, Transport properties in a spin polarized gas, i, Journal de Physique43, 197 (1982)

    1982

  22. [29]

    [37, 53–59]

    See Supplemental Material at [URL], which includes Refs. [37, 53–59]

  23. [30]

    M. D. Swallows, M. Bishof, Y. Lin, S. Blatt, M. J. Martin, A. M. Rey, and J. Ye, Suppression of collisional shifts in a strongly interacting lattice clock, Science331, 1043 (2011)

    2011

  24. [31]

    M. D. Swallows, M. J. Martin, M. Bishof, C. Benko, Y. Lin, S. Blatt, A. M. Rey, and J. Ye, Operating a 87sr optical lattice clock with high precision and at high density, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control59, 416 (2012)

    2012

  25. [32]

    Y. B. Band and A. Vardi, Collisional shifts in optical- lattice atom clocks, Phys. Rev. A74, 033807 (2006)

    2006

  26. [33]

    S. Lee, C. Y. Park, W.-K. Lee, and D.-H. Yu, Can- cellation of collisional frequency shifts in optical lattice clocks with rabi spectroscopy, New Journal of Physics18, 033030 (2016)

    2016

  27. [34]

    Barbiero, D

    M. Barbiero, D. Calonico, F. Levi, and M. G. Tarallo, Optically loaded strontium lattice clock with a single multi-wavelength reference cavity, IEEE Transactions on Instrumentation and Measurement71, 1 (2022)

    2022

  28. [35]

    Barbiero, J

    M. Barbiero, J. P. Salvatierra, M. Risaro, C. Clivati, D. Calonico, F. Levi, and M. G. Tarallo, Broadband serrodyne phase modulation for optical frequency stan- dards and spectral purity transfer, Optics Letters48, 1958 (2023)

    1958

  29. [36]

    Barbiero, M

    M. Barbiero, M. G. Tarallo, D. Calonico, F. Levi, G. Lamporesi, and G. Ferrari, Sideband-enhanced cold atomic source for optical clocks, Physical Review Applied 13, 014013 (2020)

    2020

  30. [37]

    Bouganne, M

    R. Bouganne, M. B. Aguilera, A. Dareau, E. Soave, J. Beugnon, and F. Gerbier, Clock spectroscopy of in- 7 teracting bosons in deep optical lattices, New Journal of Physics19, 113006 (2017)

    2017

  31. [38]

    Traverso, R

    A. Traverso, R. Chakraborty, Y. N. M. de Escobar, P. G. Mickelson, S. B. Nagel, M. Yan, and T. C. Killian, In- elastic and elastic collision rates for triplet states of ul- tracold strontium, Physical Review A79, 060702 (2009), arXiv:0809.0936v1 [physics.atom-ph]

    2009 arXiv

  32. [39]

    Dolde, D

    J. Dolde, D. Ganapathy, X. Zheng, S. Ma, K. Beloy, and S. Kolkowitz, Direct measurement of the 3p0 clock state natural lifetime in 87Sr, Phys. Rev. A112, 023121 (2025)

    2025

  33. [40]

    Bishof, Y

    M. Bishof, Y. Lin, M. D. Swallows, A. V. Gorshkov, J. Ye, and A. M. Rey, Resolved atomic interaction sidebands in an optical clock transition, Phys. Rev. Lett.106, 250801 (2011)

    2011

  34. [41]

    Stellmer, R

    S. Stellmer, R. Grimm, and F. Schreck, Production of quantum-degenerate strontium gases, Phys. Rev. A87, 013611 (2013)

    2013

  35. [42]

    Johansson, P

    J. Johansson, P. Nation, and F. Nori, Qutip: An open- source python framework for the dynamics of open quan- tum systems, Computer Physics Communications183, 1760 (2012)

    2012

  36. [43]

    G. J. Dick, Local oscillator induced instabilities in trapped ion frequency standards, inProceedings of the 19th Annual Precise Time and Time Interval Systems and Applications Meeting(1989) pp. 133–147

    1989

  37. [44]

    G. K. Campbell, M. M. Boyd, J. W. Thomsen, M. J. Mar- tin, S. Blatt, M. D. Swallows, T. L. Nicholson, T. Fortier, C. W. Oates, S. A. Diddams, N. D. Lemke, P. Naidon, P. Julienne, J. Ye, and A. D. Ludlow, Probing inter- actions between ultracold fermions, Science324, 360 (2009)

    2009

  38. [45]

    N. D. Lemke, J. von Stecher, J. A. Sherman, A. M. Rey, C. W. Oates, and A. D. Ludlow,p-wave cold collisions in an optical lattice clock, Phys. Rev. Lett.107, 103902 (2011)

    2011

  39. [46]

    Borkowski, Optical lattice clocks with weakly bound molecules, Phys

    M. Borkowski, Optical lattice clocks with weakly bound molecules, Phys. Rev. Lett.120, 083202 (2018)

    2018

  40. [47]

    Bettermann, N

    O. Bettermann, N. Darkwah Oppong, G. Pasqualetti, L. Riegger, I. Bloch, and S. F¨ olling, Clock-line photoasso- ciation of strongly bound dimers in a magic-wavelength lattice, Phys. Rev. A108, L041302 (2023)

    2023

  41. [48]

    J. P. Salvatierra,Advancing Optical Lattice Clocks: Ac- curate Measurements on a Bosonic System and Devel- opment of a Hybrid Cavity-Lattice Clock, Ph.D. thesis, Politecnico di Torino (2026)

    2026

  42. [49]

    Miyake, N

    H. Miyake, N. C. Pisenti, P. K. Elgee, A. Sitaram, and G. K. Campbell, Isotope-shift spectroscopy of the1S0 →3 P1 and 1S0 →3 P0 transitions in strontium, Phys. Rev. Res.1, 033113 (2019)

    2019

  43. [50]

    L.-M. Duan, E. Demler, and M. D. Lukin, Controlling Spin Exchange Interactions of Ultracold Atoms in Opti- cal Lattices, Phys. Rev. Lett.91, 090402 (2003)

    2003

  44. [51]

    C.-C. Chen, R. Takeuchi, S. Okaba, and H. Ka- tori, Narrow-line-mediated sisyphus cooling in the 3p2 metastable state of strontium, Phys. Rev. Res.7, L022076 (2025)

    2025

  45. [52]

    Comparin, F

    T. Comparin, F. Mezzacapo, M. Robert-de Saint- Vincent, and T. Roscilde, Scalable spin squeezing from spontaneous breaking of a continuous symmetry, Phys. Rev. Lett.129, 113201 (2022)

    2022

  46. [53]

    Breuer and F

    H. Breuer and F. Petruccione,The Theory of Open Quan- tum Systems(Oxford University Press, 2002)

    2002

  47. [54]

    Gonzalez-Ballestero, Tutorial: Projector approach to master equations for open quantum systems, Quantum 8, 1454 (2024)

    C. Gonzalez-Ballestero, Tutorial: Projector approach to master equations for open quantum systems, Quantum 8, 1454 (2024)

    2024

  48. [55]

    Giaccari, G

    S. Giaccari, G. Dellea, M. G. Genoni, and G. Bertaina, Higher-order adiabatic elimination in atom-cavity sys- tems and its impact on spin-squeezing generation, Quan- tum Sci. Technol.11, 035019 (2026)

    2026

  49. [57]

    C. J. Pethick and H. Smith,Bose–Einstein Condensation in Dilute Gases(Cambridge University Press, 2002)

    2002

  50. [58]

    A. L. Fetter and J. D. Walecka,Quantum Theory of Many-Particle Systems(Dover Publications, 2003)

    2003

  51. [59]

    Bishof, M

    M. Bishof, M. J. Martin, M. D. Swallows, C. Benko, Y. Lin, G. Quemener, A. M. Rey, and J. Ye, Inelastic collisions and density-dependent excitation suppression in a Sr-87 optical lattice clock, Phys. Rev. A84, 052716 (2011). 8 Supplemental Material for Measurement and control ...

    2011

  52. [60]

    Thus the single sink state|0⟩allows the pair losses to be included directly at the reduced spin-model level

    Their rate operators count the appropriate pairs: X i<j ˆJ ee† ij ˆJ ee ij = Γee 2 ˆNe( ˆNe −1), X i<j ˆJ eg,+† ij ˆJ eg,+ ij = Γeg ˆNe ˆNg,(S.32) with the second equation holding exactly strictly- speaking only in symmetrized spin manifolds. Thus the single sink state|0⟩allow...

  53. [61]

    For a clock interrogation time Tπ ≪(N 0Γee)−1 the two-body loss terms in (S.44) can be neglected, and the first definition ofδν int can be used, reducing our model to Eqs

    +χN 0w, in case a loss-weighted shift is considered at the mean-field level. For a clock interrogation time Tπ ≪(N 0Γee)−1 the two-body loss terms in (S.44) can be neglected, and the first definition ofδν int can be used, reducing our model to Eqs. (3) in the Main text. RELAXA...

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