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Transportable strontium lattice clock with $4 \times 10^{-19}$ blackbody radiation shift uncertainty

T0 review · 0 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that a trailer-mounted strontium lattice clock holds the blackbody radiation shift — normally the dominant systematic error in such clocks — to 4.0 × 10⁻¹⁹, for a total systematic uncertainty of 2.1 × 10⁻¹⁸.

desk verdict Solid, believable BBR uncertainty and total budget; the FEM patch-potential worry is minor, and the paper deserves full peer review. read the letter →

arxiv 2507.14030 v1 pith:BFOVSCUG submitted 2025-07-18 physics.atom-ph quant-ph

I. Nosske , C. Vishwakarma , T. Lücke , J. Rahm , N. Poudel , S. Weyers , E. Benkler , S. Dörscher
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C. Lisdat
This is my paper
classification physics.atom-phquant-ph PACS 06.30.Ft
keywords transportableopticalclocklatticestrontiumatomsblackbodyradiationshiftsingle-beammagneto-opticaltrapabsolutefrequencychronometricgeodesythermalshield
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 reports a transportable optical lattice clock based on $^{87}$Sr atoms with a claimed total systematic uncertainty of $2.1 \times 10^{-18}$, on par with the best laboratory strontium clocks, while operating from a trailer that can be driven between sites. Its central result is controlling the blackbody radiation (BBR) shift — usually the dominant systematic effect in strontium clocks — at the level of $4.0 \times 10^{-19}$ by interrogating the atoms inside a well-characterised cold copper shield. The thermal model of the shield is validated by measuring the clock frequency at different atomic positions and reproducing the predicted position-dependent BBR shift, and the clock's absolute frequency is measured against primary caesium fountains to be $429\,228\,004\,229\,872.951(80)$ Hz, consistent with earlier determinations. If the claims hold, mobile clocks can serve for centimetre-level chronometric geodesy and inter-institute frequency comparisons at the $10^{-18}$ level, a step toward validating a possible redefinition of the SI second.

What carries the argument

The carrying mechanism is the cold copper BBR shield together with the position-dependent shift model that describes it. Atoms are transported by a moving optical lattice into the centre of the shield, where the dominant thermal radiation comes from the shield itself; room-temperature BBR enters only through two holes of radius $0.484(6)$ mm, whose fractional solid angle $\Omega(z)/4\pi$ is computed from the measured geometry and enlarged to an effective solid angle $\Omega_{\mathrm{eff}}(z)$ through the inner coating's emissivity. The model $\Delta\nu_{\mathrm{BBR}}^{\mathrm{shield}}(z) = \Delta\nu_{\mathrm{BBR}}(T_{\mathrm{shield}})\left(1 - \frac{\Omega_{\mathrm{eff}}(z)}{4\pi}\right) + \frac{\Omega_{\mathrm{eff}}(z)}{4\pi}\Delta\nu_{\mathrm{BBR}}(T_{\mathrm{out}})$ is validated by interleaving clock stabilisations at different positions: the measured differential shift outside the shield, $-3.33(3) \times 10^{-15}$, matches the predicted $-3.32(7) \times 10^{-15}$, and propagating the parameter uncertainties yields the BBR budget that reaches $4.0 \times 10^{-19}$ at $-100\,^\circ$C.

What would settle it

Repeat the position-dependent differential frequency measurement of figure 4 with a second BBR shield of different bore geometry or coating thickness: if the residuals near the holes change in a way that shifts the inferred centre value by more than about $1 \times 10^{-19}$, the surface-potential bound — and with it the reported $4.0 \times 10^{-19}$ BBR uncertainty — would need to be enlarged.

Watch

Extended reading notes

Core claim

The paper's central claim is that a transportable strontium lattice clock can reduce the blackbody radiation shift — the leading systematic in most strontium clocks — to $4.0 \times 10^{-19}$ by moving the atoms into a 20 mm-long, high-emissivity copper shield cooled to about $-100\,^\circ$C, where the thermal environment is known to 20 mK. The BBR evaluation rests on a position-dependent model: the atoms see cold radiation from the shield plus a small, geometrically measured solid angle of room-temperature radiation through two apertures, corrected for inner-wall emissivity, and the model is checked against interleaved frequency measurements at different positions in and around the shield. With this evaluation the total systematic uncertainty is $2.1 \times 10^{-18}$, the instability is $5 \times 10^{-16}/\sqrt{\tau/\mathrm{s}}$ with a transportable clock laser, and comparison with caesium fountain clocks gives $429\,228\,004\,229\,872.951(80)$ Hz for the $^1\mathrm{S}_0 \rightarrow {}^3\mathrm{P}_0$ transition, in agreement with previous measurements.

Load-bearing premise

The load-bearing premise is that stray electric fields from the shield's inner surfaces do not reach the atoms: the $-1 \times 10^{-19}$ DC Stark bound comes from a simulation whose free parameters were fitted to the same residual measurements it then explains, so if real surface potentials extend further into the shield than the tuned model assumes, the $4.0 \times 10^{-19}$ blackbody uncertainty would be too small.

Editorial extensions

If this is right

  • The BBR shift uncertainty of $4.0 \times 10^{-19}$ is smaller than that of most stationary strontium lattice clocks, removing the field's usual dominant error from the mobile system's budget.
  • At a total systematic uncertainty of $2.1 \times 10^{-18}$, the relativistic redshift from about one centimetre of height difference is already resolvable, so the clock becomes a practical tool for chronometric geodesy.
  • The measured absolute frequency $429\,228\,004\,229\,872.951(80)$ Hz agrees with the established $^{87}$Sr transition frequency, qualifying the transportable clock as a trustworthy reference for inter-institute comparisons.
  • With $5 \times 10^{-16}/\sqrt{\tau/\mathrm{s}}$ instability, systematic effects can be re-evaluated quickly after each move, turning recharacterisation into a routine step rather than a long campaign.
  • The design is stated to be extendable, with a longer shield and $T_{\mathrm{shield}} \lesssim 100$ K projected to bring BBR uncertainty toward the $10^{-20}$ regime.

Reading between the lines

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

  • If the centre-of-shield surface-potential bound survives scrutiny, the moving-lattice plus cold-shield architecture should transfer to other lattice-trapped species, and coating the bores before assembly would let future clocks avoid the fitted-model step entirely.
  • The position-scan method itself could be reused as an in-situ diagnostic: interleaved frequency measurements versus atomic position simultaneously verify the thermal model and expose stray-field sources as sharp features at hole edges long before they reach the centre.
  • A concrete near-term test of the transportability claim is a two-site comparison over existing fibre links: the stated instability would resolve $10^{-18}$-level agreement between sites in hours, far faster than earlier mobile-clock campaigns.
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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

0 major / 5 minor

Summary. The manuscript presents the second-generation PTB transportable 87Sr optical lattice clock, Sr4. The central claims are (i) a blackbody radiation (BBR) shift uncertainty of 4 × 10−19 at the operating shield temperature of −100 °C, achieved by interrogating atoms inside a cold 20-mm copper shield with characterized apertures; (ii) a total systematic uncertainty of 2.1 × 10−18 from the itemized budget in Table 1; and (iii) an absolute frequency of 429 228 004 229 872.951(80) Hz for the 1S0→3P0 transition, measured against PTB's caesium fountains with a fractional uncertainty of 1.9 × 10−16. The spatial BBR model is tested by differential frequency-shift measurements versus atom position at −50.1 °C, where the measured mean shift agrees with a parameter-free model prediction.

Significance. If correct, the results are significant: the BBR shift, usually the leading systematic in strontium lattice clocks, is controlled here at a level comparable to the best laboratory systems while the clock remains transportable, and the total uncertainty is at the 10−18 scale needed for chronometric geodesy and inter-institute comparisons. The paper is notably transparent: the BBR model is benchmarked externally, the uncertainty budget in Table 1 is internally consistent (the quadrature sum reproduces 2.1 × 10−18), and the absolute frequency agrees with previous determinations. The differential BBR measurement in Fig. 4 is a particularly strong piece of evidence because it compares data with a parameter-free model prediction rather than a fitted curve.

minor comments (5)
  1. [Section 5, Appendices C and D] The text repeatedly refers to 'table 5' for the absolute-frequency measurement data, but the measurement results are in Table 2 and no Table 5 exists in the manuscript. Please correct all such cross-references.
  2. [Section 3, Fig. 4] The model of Eq. (4) is experimentally validated only at Tshield = −50.1 °C, whereas the claimed 4 × 10−19 uncertainty is for operation at −100 °C. The authors should explicitly acknowledge this verification gap and, ideally, add a second shield-temperature check or an explicit argument that the residual T-dependence beyond Eq. (4) is negligible.
  3. [Section 3, patch potentials] The FEM simulation used to bound the residual surface-potential shift at the shield centre is fitted to the residuals in Fig. 4(b), e.g., via the 'linear variation of the surface potential along the bore and an offset from the hole axis'. This model dependence should be stated more prominently; although the resulting DC-Stark entry in Table 1 is small, a conservative upper bound independent of the fit would strengthen the statement that no unrecognized shift affects the BBR evaluation.
  4. [Section 3, Eq. (1)] The statement that the scaled η coefficients agree with the full calculation of Ref. [6] within 1 × 10−19 relies on private communication [43]; including the comparison curve or a brief calculation summary would make the BBR response component of the budget fully self-contained.
  5. [Figure 4] The shading references ('light-yellow', 'dark-yellow', 'red-shaded') are hard to distinguish in print; consider using hatching or labelled regions directly in the figure.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the BBR uncertainty, total systematic uncertainty, and absolute frequency claims are externally benchmarked; the sole model-fitted element (patch-potential DC Stark bound) is small, conservative, and non-central.

full rationale

The paper's central claims—a 4.0e-19 BBR shift uncertainty at -100 C, a 2.1e-18 total systematic uncertainty, and an absolute 87Sr clock frequency of 429 228 004 229 872.951(80) Hz with 1.9e-16 fractional uncertainty—rest on a derivation chain that is self-contained against external benchmarks. The BBR shift is computed from directly measured quantities (Tshield with 20 mK uncertainty from Pt100 calibration, bridge, and an FEM temperature-gradient model; hole radii measured by CMM and microscope in Appendix B; emissivity certified by the supplier) and externally anchored atomic response coefficients (dynamic/static values from [6], M1 from [44,45]). The position-dependent BBR model of Eq. (4) is validated against interleaved clock measurements at -50 C: measured -3.33(3)e-15 versus expected -3.32(7)e-15, a parameter-free agreement. The patch-potential FEM simulation is fitted to the Fig. 4(b) residuals near the hole edges, but the resulting DC Stark bound of -1(1)e-19 is small, conservative (uncertainty set equal to magnitude), consistent with the directly observed small residuals at the shield centre, and non-central: it contributes only 0.1e-18 to the 2.1e-18 total, so even a tenfold miss would leave the headline claims intact. The absolute frequency measurement compares the clock to the primary caesium fountains CSF1 and CSF2 at PTB, independent external references, and the result agrees with the externally compiled value of [61]. Self-citations ([13], [28], [42], [59]) document the predecessor clock, the clock laser, interpolation coefficients (rescaled to the external value of [6]), and the measurement procedure; none bears the weight of the central claims. No reduction by construction and no fitted input renamed as a prediction was found. The main verification gap—direct BBR-model validation at the -100 C operating point rather than only at -50 C—is a missing check, not a demonstrated circularity.

Assumptions & free parameters 4 free parameters · 9 assumptions · 0 invented entities

The central claims depend mainly on external benchmarks (atomic response coefficients [6,41,52,54,55], collision shift coefficient [56], supplier-certified emissivity, metrology of the bore radii) and on the authors' own transparency about remaining model dependence. The genuinely paper-specific choices are tuned FEM parameters: the absorbed lattice power adjusted to reproduce the measured shield heating, and the per-bore surface-potential profiles fitted to the figure 4(b) residuals. These determine the temperature-gradient uncertainty (part of the 20 mK Tshield budget) and the -1×10^-19 residual patch-potential bound. No new physical entities are introduced.

free parameters (4)
  • Dynamic BBR scaling coefficients η6, η8, η10 = η6 = -0.13216 Hz, η8 = -0.01231 Hz, η10 = -0.00858 Hz
    Eq. (1): these set the dynamic BBR contribution at the operating temperature. They are scaled from the authors' earlier work [42] to match the external 300 K value -153.06(33) mHz from [6]; the agreement with the full calculation below 300 K is asserted via private communication [43].
  • FEM absorbed lattice power = Adjusted to reproduce the observed ~100 mK shield heating; equivalent to ~1% lattice power absorption
    Section 3, FEM temperature simulation: 'To account for the heating by the lattice laser, we adjust the absorbed power to match the observed temperature increase of the shield.' This tuned value determines the 53 mK temperature-gradient estimate that contributes to the 20 mK Tshield uncertainty and thus to the headline 4×10^-19 BBR uncertainty.
  • Surface potential profile, bore at z>0 = Varying surface potential on the inner edge of the bore (reduced coating thickness)
    Section 3, figure 4(b): the outer-edge peaks are 'well reproduced by a finite element method (FEM) simulation that incorporates a small varying surface potential'. The profile is chosen to fit the residuals.
  • Surface potential profile, bore at z<0 = Linear surface-potential variation along the bore plus an offset from the hole axis
    Section 3: 'These can be modelled if a linear variation of the surface potential along the bore and an offset from the hole axis are assumed.' The fitted parameters determine the -1×10^-19 residual patch-potential bound at the shield centre.
assumptions (9)
  • domain assumption Decomposition of the BBR shift into a static T^4 term plus a dynamic term with temperature scaling f(T/T0) = (η6 + η8 (T/T0)^2 + η10 (T/T0)^4) / (η6 + η8 + η10)
    Section 3, eq. (1). This functional form extrapolates the dynamic shift from 300 K down to roughly 173 K; an error in the temperature dependence would shift the whole BBR correction.
  • domain assumption Inner shield coating emissivity εin = 0.926(43) from the supplier-certified hemispherical reflectance, and negligible emissivity εout ≈ 0.03 of the polished outer copper surfaces
    Section 3: these inputs feed the effective solid-angle model in eq. (3), which determines how much room-temperature BBR reaches the atoms.
  • standard math Effective solid-angle formula (eq. 3) for outside BBR entering through the holes and scattering off the inner walls
    Section 3, eq. (3), taken from [46,47]; it converts the geometric solid angle into an effective one using the inner emissivity.
  • domain assumption Bore radii reff = 0.484(6) mm, atom position z = 0(0.5) mm, and shield length 20.0(0.1) mm determined by coordinate measurement and microscopy
    Appendix B, table BI: these metrology inputs determine the fractional solid angle and hence the outside-BBR contribution and its uncertainty.
  • domain assumption Atomic BBR response coefficients: dynamic coefficient -153.06(33) mHz at 300 K from [6], static coefficient from [41]
    Section 3: these external coefficients anchor the absolute BBR shift estimate at the operating temperature.
  • domain assumption Lattice light shift model of [53] with differential polarisability, hyperpolarisability and E2-M1 coefficients from [52] and [54]
    Section 4.2: the largest uncertainty term (1.7×10^-18) is computed from this model and the sideband-spectroscopy population distribution.
  • domain assumption Density shift scaling ∝ N U^(3/4) taken from [51]
    Section 4.1: used to scale the measured density shift between different atom numbers and trap depths.
  • domain assumption H2 background-gas collision shift coefficient -30(3)×10^-18 s/τtrap from [56], with measured 1/e trap lifetimes of 9-15 s bounding the collision-limited lifetime
    Section 4.4: the background-gas shift of -2.3(1.0)×10^-18 is estimated from this coefficient and the measured lifetimes, which the text notes are lower bounds.
  • domain assumption Second-order Zeeman shift coefficient from [55] converts the measured mF = ±9/2 splitting into the Zeeman shift
    Section 4.3: the splitting is tracked during clock stabilization and converted to a shift using the external coefficient.

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Cite this review

Pith. "Pith review of Transportable strontium lattice clock with $4 \times 10^{-19}$ blackbody radiation shift uncertainty." pith.science (2026). https://pith.science/paper/BFOVSCUG

@misc{pith2026250714030,
  author       = {Pith},
  title        = {Pith review of: Transportable strontium lattice clock with $4 \times 10^-19$ blackbody radiation shift uncertainty},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BFOVSCUG}},
  note         = {Machine review of arXiv:2507.14030}
}
abstract

We describe a transportable optical lattice clock based on the $^1\mathrm{S}_0 \rightarrow {^3\mathrm{P}_0}$ transition of lattice-trapped $^{87}$Sr atoms with a total systematic uncertainty of $2.1 \times 10^{-18}$. The blackbody radiation shift, which is the leading systematic effect in many strontium lattice clocks, is controlled at the level of $4.0 \times 10^{-19}$, as the atoms are interrogated inside a well-characterised, cold thermal shield. Using a transportable clock laser, the clock reaches a frequency instability of about $5 \times 10^{-16}/\sqrt{\tau/\mathrm{s}}$, which enables fast reevaluations of systematic effects. By comparing this clock to the primary caesium fountain clocks CSF1 and CSF2 at Physikalisch-Technische Bundesanstalt, we measure the clock transition frequency with a fractional uncertainty of $1.9\times 10^{-16}$, in agreement with previous results. The clock was successfully transported and operated at different locations. It holds the potential to be used for geodetic measurements with centimetre-level or better height resolution and for accurate inter-institute frequency comparisons.

Figures

Figures reproduced from arXiv: 2507.14030 by the authors.

Figure 1
Figure 1. Layout of the core components of the physics package. (a) A model of the pyramid MOT (1) and the BBR shield (2) in the centre of the main vacuum chamber, together with all laser beams except the MOT cooling beam. For the vertical beams the linear polarisation direction is indicated, where this is relevant. The upper state hyperfine levels of 87Sr addressed by the 689 nm beams are also given. The upper inset shows th… view at source ↗
Figure 2
Figure 2. Spectroscopy of and stabilisation on the 698 nm clock transition. (a) Scans of the clock transition of atomic samples spin-polarised in the mF = ±9/2 states with 500 ms Rabi interrogation pulses. The solid lines are fits with the expected line shape. (b) Frequency stability of a comparison between the transportable lattice clock Sr4 and the laboratory clock Sr3 [37], which is much more stable thanks to an ultra-stab… view at source ↗
Figure 3
Figure 3. Cut through the BBR shield in the xz plane with indications of the hole positions, hole radii, temperatures and emissivities that are relevant for the BBR shift determination. also BBR from the outside that is scattered on the inner walls may interact with the atoms. This increases the effective solid angle under which the atoms see the holes to [46, 47] Ωeff(z) 4π = 1 1 +  4π Ω(z) − 1  ϵin . (3) The position-depe… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Differential frequency shifts in and around the BBR shield. (a) Position dependent fractional frequency shift relative to the centre of the BBR shield at Tshield = −50 ◦C and Tout = 21 ◦C (dots). The red curve is the expected differential BBR shift according to (4). Th…
Figure 5
Figure 5. Figure 5: FEM simulation of the temperature of the BBR shield. combined residual shift from the two inner hole edges at the BBR shield centre is up to about −1 × 10−19 . We expect temperature inhomogeneities of the BBR shield due to residual absorption of room temperature BBR an…
Figure 6
Figure 6. Figure 6: BBR shift uncertainty contributions associated with uncertainties of different quantities versus Tshield. The solid (dashed) lines denote uncertainties related to the BBR shift from Tshield (Tout). thermal inhomogeneity caused by room temperature BBR absorption alone. …

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Works this paper leans on

76 extracted references · 74 canonical work pages

  1. [1]

    Huntemann N, Sanner C, Lipphardt B, Tamm C and Peik E 2016 Phys. Rev. Lett.116(6) 063001

    work page 2016

  2. [2]

    McGrew W F, Zhang X, Fasano R J, Sch¨ affer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milan G, Schioppo M, Yoon T H and Ludlow A D 2018 Nature 564 87–90 Transportable strontium lattice clock with4 × 10−19 BBR shift uncertainty 21 qi qj r(qi, qj) ¯ν(Sr|CSF1) ∆b,Sr 0.019 ¯ν(Sr|CSF1) ∆b,CSF1 −0.706 ¯ν(Sr|CSF2) ∆b,Sr 0.038 ¯ν(Sr|CSF2) ∆b,CSF2 −0.845 ¯ν(...

    work page 2018

  3. [3]

    Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B and Leibrandt D R 2019 Phys. Rev. Lett.123 033201

    work page 2019

  4. [4]

    Huang Y, Zhang B, Zeng M, Hao Y, Ma Z, Zhang H, Guan H, Chen Z, Wang M and Gao K 2022 Phys. Rev. Applied17(3) 034041

    work page 2022

  5. [5]

    Tofful A, Baynham C F A, Curtis E A, Parsons A O, Robertson B I, Schioppo M, Tunesi J, Margolis H S, Hendricks R J, Whale J, Thompson R C and Godun R M 2024 Metrologia 61 045001

    work page 2024

  6. [6]

    Aeppli A, Kim K, Warfield W, Safronova M S and Ye J 2024 Phys. Rev. Lett.133(2) 023401

    work page 2024

  7. [7]

    Arnold K J, Bustabad S, Qichen Q, Zhang Z, Zhao Q and Barrett M D 2024 Validating a lutetium frequency reference arXiv:2404.16414 [physics.atom-ph]

    work page Pith review arXiv 2024

  8. [8]

    Hausser H N, Keller J, Nordmann T, Bhatt N M, Kiethe J, Liu H, Richter I M, von Boehn M, Rahm J, Weyers S, Benkler E, Lipphardt B, D¨ orscher S, Stahl K, Klose J, Lisdat C, Filzinger M, Huntemann N, Peik E and Mehlst¨ aubler T E 2025Phys. Rev. Lett.134(2) 023201

    work page

Show all 76 references
  1. [9]

    Dimarcq N, Gertsvolf M, Mileti G, Bize S, Oates C W, Peik E, Calonico D, Ido T, Tavella P, Meynadier F, Petit G, Panfilo G, Bartholomew J, Defraigne P, Donley E A, Hedekvist P O, Sesia I, Wouters M, Dub´ e P, Fang F, Levi F, Lodewyck J, Margolis H S, Newell D, Slyusarev S, Wey...

    2024

  2. [10]

    ICON: International Clock and Oscillator Networking and Collaboration:, Amy-Klein A, Benkler E, Blond´ e P, Bongs K, Cantin E, Chardonnet C, Denker H, D¨ orscher S, Feng C H, Gaudron J O, Gill P, Hill I R, Huang W, Johnson M Y H, Kale Y B, Katori H, Klose J, Kronj¨ ager J, Kuh...

    2024 arXiv

  3. [11]

    Mehlst¨ aubler T, Grosche G, Lisdat C, Schmidt P and Denker H 2018 Rep. Prog. Phys.81 064401

    2018

  4. [12]

    Denker H, Timmen L, Voigt C, Weyers S, Peik E, Margolis H S, Delva P, Wolf P and Petit G 2018 Journal of Geodesy5 487–516 ISSN 1432-1394

    2018

  5. [13]

    Koller S B, Grotti J, Vogt S, Al-Masoudi A, D¨ orscher S, H¨ afner S, Sterr U and Lisdat C 2017 Phys. Rev. Lett.118 073601

    2017

  6. [14]

    Origlia S, Pramod M S, Schiller S, Singh Y, Bongs K, Schwarz R, Al-Masoudi A, D¨ orscher S, Herbers S, H¨ afner S, Sterr U and Lisdat C 2018 Phys. Rev. A98 053443

    2018

  7. [15]

    Huang Y, Zhang H, Zhang B, Hao Y, Guan H, Zeng M, Chen Q, Lin Y, Wang Y, Cao S, Liang K, Fang F, Fang Z, Li T and Gao K 2020 Phys. Rev. A102(5) 050802(R) Transportable strontium lattice clock with4 × 10−19 BBR shift uncertainty 22

    2020

  8. [16]

    Quantum Technol.4 2100015

    Ohmae N, Takamoto M, Takahashi Y, Kokubun M, Araki K, Hinton A, Ushijima I, Muramatsu T, Furumiya T, Sakai Y, Moriya N, Kamiya N, Fujii K, Muramatsu R, Shiimado T and Katori H 2021 Adv. Quantum Technol.4 2100015

    2021

  9. [17]

    Stuhler J, Abdel Hafiz M, Arar B, Bawamia A, Bergner K, Biethahn M, Brakhane S, Didier A, Fortagh J, Halder M, Holzwarth R, Huntemann N, Johanning M, J¨ ordens R, Kaenders W, Karlewski F, Kienle F, Krutzik M, Lessing M, Mehlst¨ aubler T, Meschede D, Peik E, Peters A, Schmidt P...

  10. [18]

    Guo F, Tan W, Zhou C h, Xia J, Chen Y x, Liang T, Liu Q, Liu Y, He D j, Zhou Y z, Wang W h, Shen Y, Zou H x and Chang H 2021 AIP Advances 11 125116

    2021

  11. [19]

    Technol.7 045004

    Kale Y B, Singh A, Gellesch M, Jones J M, Morris D, Aldous M, Bongs K and Singh Y 2022 Quantum Sci. Technol.7 045004

    2022

  12. [20]

    Liu D X, Cao J, Yuan J B, Cui K F, Yuan Y, Zhang P, Chao S J, Shu H L and Huang X R 2023 Chin. Phys. B32 010601

    2023

  13. [21]

    Zeng M, Huang Y, Zhang B, Hao Y, Ma Z, Hu R, Zhang H, Chen Z, Wang M, Guan H and Gao K 2023 Phys. Rev. Appl.19(6) 064004

    2023

  14. [22]

    thesis University of Colorado at Boulder

    Brand W J 2024 A Transportable Ytterbium Optical Lattice Clock With Eighteen Digits of Accuracy Ph.D. thesis University of Colorado at Boulder

    2024

  15. [23]

    Hobson R, Bowden W, Silva A, Baynham C F A, Margolis H S, Baird P E G, Gill P and Hill I R 2020 Metrologia 57 065026

    2020

  16. [24]

    Goti I, Condio S, Clivati C, Risaro M, Gozzelino M, Costanzo G A, Levi F, Calonico D and Pizzocaro M 2023 Metrologia 60 035002

    2023

  17. [25]

    Li J, Cui X Y, Jia Z P, Kong D Q, Yu H W, Zhu X Q, Liu X Y, Wang D Z, Zhang X, Huang X Y, Zhu M Y, Yang Y M, Hu Y, Liu X P, Zhai X M, Liu P, Jiang X, Xu P, Dai H N, Chen Y A and Pan J W 2024 Metrologia 61 015006

    2024

  18. [26]

    Ushijima I, Takamoto M, Das M, Ohkubo T and Katori H 2015 Nature Photonics 9 185–189

    2015

  19. [27]

    2025 arXiv preprint arXiv:2506.05304

    Hassan Y S, Beloy K, Siegel J L, Kobayashi T, Swiler E, Grogan T, Brown R C, Rojo T, Bothwell T, Hunt B D et al. 2025 arXiv preprint arXiv:2506.05304

    2025 arXiv

  20. [28]

    Lett.47 5441–5444

    Herbers S, H¨ afner S, D¨ orscher S, L¨ ucke T, Sterr U and Lisdat C 2022Opt. Lett.47 5441–5444

  21. [29]

    Express 28 16407–16416

    H¨ afner S, Herbers S, Vogt S, Lisdat C and Sterr U 2020 Opt. Express 28 16407–16416

    2020

  22. [30]

    Weyers S, Gerginov V, Kazda M, Rahm J, Lipphardt B, Dobrev G and Gibble K 2018 Metrologia 55 789–805

    2018

  23. [31]

    Schioppo M, Kronj¨ ager J, Silva A, Ilieva R, Paterson J W, Baynham C F A, Bowden W, Hill I R, Hobson R, Vianello A, Dovale- ´Alvarez M, Williams R A, Marra G, Margolis H S, Amy-Klein A, Lopez O, Cantin E, ´Alvarez-Mart ´ ınez H, Le Targat R, Pottie P E, Quintin N, Legero T, H...

    2022

  24. [32]

    Clivati C, Aiello R, Bianco G, Bortolotti C, Natale P D, Sarno V D, Maddaloni P, Maccaferri G, Mura A, Negusini M, Levi F, Perini F, Ricci R, Roma M, Amato L S, de Cumis M S, Stagni M, Tuozzi A and Calonico D 2020 Optica 7 1031–1037

    2020

  25. [33]

    Express27 36886–36902

    Benkler E, Lipphardt B, Puppe T, Wilk R, Rohde F and Sterr U 2019Opt. Express27 36886–36902

  26. [34]

    Hill I R, Ovchinnikov Y B, Bridge E M, Curtis E A and Gill P 2014 J. Phys. B: At. Mol. Phys. 47 075006

    2014

  27. [35]

    Rep.9 11704

    Bowden W, Hobson R, Hill I R, Vianello A, Schioppo M, Silva A, Margolis H S, Baird P E G and Gill P 2019 Sci. Rep.9 11704

    2019

  28. [36]

    Mukaiyama T, Katori H, Ido T, Li Y and Kuwata-Gonokami M 2003 Phys. Rev. Lett.90 113002

    2003

  29. [37]

    thesis QUEST-Leibniz-Forschungsschule der Gottfried Wilhelm Leibniz Universit¨ at Hannover

    Schwarz R 2022 A cryogenic Strontium lattice clockPh.D. thesis QUEST-Leibniz-Forschungsschule der Gottfried Wilhelm Leibniz Universit¨ at Hannover

    2022

  30. [38]

    Matei D G, Legero T, H¨ afner S, Grebing C, Weyrich R, Zhang W, Sonderhouse L, Robinson J M, Ye J, Riehle F and Sterr U 2017 Phys. Rev. Lett.118 263202

    2017

  31. [39]

    Falke S, Schnatz H, Vellore Winfred J S R, Middelmann T, Vogt S, Weyers S, Lipphardt B, Grosche Transportable strontium lattice clock with4 × 10−19 BBR shift uncertainty 23 G, Riehle F, Sterr U and Lisdat C 2011 Metrologia 48 399–407

    2011

  32. [40]

    Al-Masoudi A, D¨ orscher S, H¨ afner S, Sterr U and Lisdat C 2015Phys. Rev. A92 063814

  33. [41]

    Middelmann T, Falke S, Lisdat C and Sterr U 2012 Phys. Rev. Lett.109(26) 263004

    2012

  34. [42]

    Lisdat C, D¨ orscher S, Nosske I and Sterr U 2021 Phys. Rev. Research3(4) L042036

    2021

  35. [43]

    Kim K, Aeppli A and Ye J 2025 private communication

    2025

  36. [44]

    Porsev S G and Derevianko A 2006 Phys. Rev. A74 020502(R)

    2006

  37. [45]

    Tang Z M, Wei Y F, Sahoo B K, Li C B, Yang Y, Zou Y and Huang X R 2024 Phys. Rev. A110 043108

    2024

  38. [46]

    Middelmann T, Lisdat C, Falke S, Vellore Winfred J S R, Riehle F and Sterr U 2011 IEEE Trans. Instrum. Meas. 60 2550–2557

    2011

  39. [47]

    Abdel-Hafiz M, Ablewski P, Al-Masoudi A, ´Alvarez Mart ´ ınez H, Balling P, Barwood G, Benkler E, Bober M, Borkowski M, Bowden W, Ciury lo R, Cybulski H, Didier A, Doleˇ zal M, D¨ orscher S, Falke S, Godun R M, Hamid R, Hill I R, Hobson R, Huntemann N, Le Coq Y, Le Targat R, L...

    2019 arXiv

  40. [48]

    2008 Evaluation of measurement data – guide to the expression of uncertainty in measurement JCGM 100:2008 URL http://www.bipm.org/utils/common/documents/jcgm/ JCGM_100_2008_E.pdf

    2008

  41. [49]

    Gaiser C, Fellmuth B, Gavioso R M, Kalemci M, Kytin V, Nakano T, Pokhodun A, Rourke P M C, Rusby R, Sparasci F, Steur P P M, Tew W L, Underwood R, White R, Yang I and Zhang J 2022 J. Phys. Chem. Ref. Data51 043105

    2022

  42. [50]

    Precise Time and Time Interval Meeting, Redondo Beach, 1987ADA502386 (Washington, DC: U.S

    Dick G J 1988 Local oscillator induced instabilities in trapped ion frequency standards Proceedings of 19th Annu. Precise Time and Time Interval Meeting, Redondo Beach, 1987ADA502386 (Washington, DC: U.S. Naval Observatory) pp 133–147 URL https://apps.dtic.mil/sti/ citations/ADA502386

    1988

  43. [51]

    Ultrason

    Swallows M, Martin M, Bishof M, Benko C, Lin Y, Blatt S, Rey A and Ye J 2012 IEEE Trans. Ultrason. Ferroelectr. Freq. Control59 416 – 425

    2012

  44. [52]

    Ushijima I, Takamoto M and Katori H 2018 Phys. Rev. Lett.121(26) 263202

    2018

  45. [53]

    Brown R C, Phillips N B, Beloy K, McGrew W F, Schioppo M, Fasano R J, Milani G, Zhang X, Hinkley N, Leopardi H, Yoon T H, Nicolodi D, Fortier T M and Ludlow A D 2017 Phys. Rev. Lett. 119(25) 253001

    2017

  46. [54]

    Kim K, Aeppli A, Bothwell T and Ye J 2023 Phys. Rev. Lett.130(11) 113203

    2023

  47. [55]

    Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, Tew W L, Ye J and Kennedy C J 2019 Metrologia 56 065004

    2019

  48. [56]

    Alves B X R, Foucault Y, Vallet G and Lodewyck J 2019 Background gas collision frequency shift on lattice-trapped strontium atoms 2019 Joint Conference of the IEEE International Frequency Control Symposium and European Frequency and Time Forum (EFTF/IFC)(Orlando, FL, USA: IEEE) pp 1–2

    2019

  49. [57]

    Muniz J A, Young D J, Cline J R K and Thompson J K 2021 Phys. Rev. Research3(2) 023152

    2021

  50. [58]

    Lu X T, Guo F, Liu Y Y, Xia J J, Zhao G D, Chen Y X, Wang Y B, Lu B Q and Chang H 2024 Physical Review Applied21 024042

    2024

  51. [59]

    Schwarz R, D¨ orscher S, Al-Masoudi A, Benkler E, Legero T, Sterr U, Weyers S, Rahm J, Lipphardt B and Lisdat C 2020 Phys. Rev. Research2(3) 033242

    2020

  52. [60]

    Grebing C, Al-Masoudi A, D¨ orscher S, H¨ afner S, Gerginov V, Weyers S, Lipphardt B, Riehle F, Sterr U and Lisdat C 2016 Optica 3 563–569

    2016

  53. [61]

    Margolis H S, Panfilo G, Petit G, Oates C, Ido T and Bize S 2024 Metrologia 61 035005

    2024

  54. [62]

    Pavlis N K and Weiss M A 2017 Metrologia 54 535

    2017

  55. [63]

    Grotti J, Koller S, Vogt S, H¨ afner S, Sterr U, Lisdat C, Denker H, Voigt C, Timmen L, Rolland A, Baynes F N, Margolis H S, Zampaolo M, Thoumany P, Pizzocaro M, Rauf B, Bregolin F, Transportable strontium lattice clock with4 × 10−19 BBR shift uncertainty 24 Tampellini A, Barb...

  56. [64]

    Lee J, Kwon J H, Park C Y, Kim H, Choi I M, Chung J W and Lee W K 2024 Metrologia 61 015008

    2024

  57. [65]

    Tanaka Y and Katori H 2021 Journal of Geodesy95 1–14

    2021

  58. [66]

    Takamoto M, Tanaka Y and Katori H 2022 Appl. Phys. Lett.120 140502

    2022

  59. [67]

    Adv.8 eadc9242

    Aeppli A, Chu A, Bothwell T, Kennedy C J, Kedar D, He P, Rey A M and Ye J 2022 Sci. Adv.8 eadc9242

    2022

  60. [68]

    Heinz A, Park A J, ˇSanti´ c N, Trautmann J, Porsev S G, Safronova M S, Bloch I and Blatt S 2020 Phys. Rev. Lett.124(20) 203201

    2020

  61. [69]

    Aeppli A, Kim K, Warfield W, Safronova M S and Ye J 2024 Phys. Rev. Lett. 133(2) 023401 URL https://journals.aps.org/prl/supplemental/10.1103/PhysRevLett. 133.023401/supplementary.pdf

    2024 doi

  62. [70]

    Hunter L R, Walker W A and Weiss D S 1986 Phys. Rev. Lett.56 823–826

    1986

  63. [71]

    Bauschlicher Jr C W, Langhoff S R and Partridge H 1985 J. Phys. B: At. Mol. Phys.18 1523–1532

    1985

  64. [72]

    zu Putlitz G 1963 Zeitschrift f¨ ur Physik175 543–552

    1963

  65. [73]

    Beenakker J J M and Swenson C A 1955 Rev. Sci. Instrum.26 1204–1205

    1955

  66. [74]

    Ultrason

    Dawkins S T, McFerran J J and Luiten A N 2007 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 918–925

    2007

  67. [75]

    Benkler E, Lisdat C and Sterr U 2015 Metrologia 52 565

    2015

  68. [76]

    Margolis H and Pizzocaro M 2020 Guidelines on the evaluation and reporting of corre- lation coefficients between frequency ratio measurements Tech. rep. 18SIB05 ROCIT URL http://empir.npl.co.uk/rocit/wp-content/uploads/sites/52/2021/02/ROCIT_ guidelines_on_correlations.pdf

    2020

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.