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arxiv: 2606.23151 · v2 · pith:MONQCGRKnew · submitted 2026-06-22 · ⚛️ physics.atom-ph

An Al^+ clock with 1.6times10⁻¹⁸ systematic uncertainty and its frequency ratios

Fabian Dawel , Johannes Kramer , Derwell Drapier , Lennart Pelzer , Kai Dietze , Mirza A. Ali , Marek Hild , Vincent Barb\'e
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Steven A. King Joshua Klose Kilian Stahl Johannes Rahm Navraj Poudel S\"oren D\"orscher Stefan Weyers Erik Benkler Christian Lisdat Piet O. Schmidt
This is my paper

Pith reviewed 2026-06-26 06:24 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords optical clockaluminum ionsystematic uncertaintyfrequency ratiostrontium clockcaesium fountainsecond redefinitionsingle ion clock
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The pith

An aluminum-ion clock reaches 1.6×10^{-18} total systematic uncertainty through full shift evaluation.

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

The paper establishes that a single trapped ^{27}Al^+ ion clock can be evaluated for all major systematic frequency shifts to a combined fractional uncertainty of 1.6×10^{-18}. This uncertainty is set primarily by the precision of atomic coefficients for effects such as polarizabilities and by background gas collision rates. The absolute frequency is tied to caesium fountain clocks and the ratio to a strontium lattice clock is measured directly. These measurements supply an independent data point for optical frequency comparisons across laboratories. The work supports efforts to base a future definition of the second on optical transitions by demonstrating achievable accuracy in one candidate system.

Core claim

The evaluated total systematic fractional frequency uncertainty of the ^{27}Al^+ clock is 1.6×10^{-18}, with the absolute frequency determined as ν_{Al^+}=1 121 015 393 207 859.19(24) Hz by comparison to two caesium fountains and the frequency ratio to the ^{87}Sr clock measured as ν_{Al^+}/ν_{^{87}Sr}=2.611 701 431 781 462 668(36). The ratio differs by 8.6σ from the 2021 BACON value and 1.2σ from the 2025 value.

What carries the argument

Full evaluation of systematic frequency shifts for the single-ion Al^+ clock, incorporating corrections from blackbody radiation, electric quadrupole shifts, and collision effects using measured or calculated atomic coefficients.

If this is right

  • The reported uncertainty level allows the Al+ clock to serve as a reference in a future optical redefinition of the second.
  • The measured frequency ratio provides an independent consistency check between single-ion and lattice optical clocks.
  • Discrepancies with prior ratio values highlight the value of repeated measurements at separate institutions to identify unaccounted effects.
  • Limits from atomic coefficient accuracy and gas collisions indicate the main technical barriers to reaching 10^{-19} uncertainty in this system.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the observed ratio difference persists in future comparisons, it would point to a need for refined modeling of one or more shift mechanisms in the comparison chain.
  • Improved theoretical calculations of the Al+ atomic coefficients could directly lower the dominant uncertainty term without changes to the experimental apparatus.
  • The single-ion approach demonstrated here could be applied to other species with simpler level structures to test whether similar uncertainty budgets are reachable.

Load-bearing premise

The atomic coefficients needed to calculate the systematic shifts, such as polarizabilities and quadrupole moments, are known accurately enough that they do not push the total uncertainty above the reported 1.6×10^{-18}.

What would settle it

A new measurement of the Al+ to Sr frequency ratio that lies outside the stated uncertainty interval of the reported value while agreeing with one of the earlier BACON results within 3σ, or a direct test showing the background gas collision uncertainty exceeds its budgeted contribution.

Figures

Figures reproduced from arXiv: 2606.23151 by Christian Lisdat, Derwell Drapier, Erik Benkler, Fabian Dawel, Johannes Kramer, Johannes Rahm, Joshua Klose, Kai Dietze, Kilian Stahl, Lennart Pelzer, Marek Hild, Mirza A. Ali, Navraj Poudel, Piet O. Schmidt, S\"oren D\"orscher, Stefan Weyers, Steven A. King, Vincent Barb\'e.

Figure 1
Figure 1. Figure 1: Simplified sketch of the frequency ratio mea [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a)-c) Modulation index measured from three [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: a) Shows the daily mean of the frequency ra [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Laser setup used in the experiment. a) shows the projection on the xz plane, while b) shows the projection [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Beam 1 is propagating along the z-axis. For beam 2 the coordinate system is rotated, such that it is in the x − z plane. The ion’s velocity direction is described by two angles θ and φ. Note the change in coordinate system compared to [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Probability to see a certain first-order Doppler shift depending on the direction of the ion velocity. In [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Measurement of the first-order Doppler shift. The upper plot shows all frequency measurement points. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Achieved mean motional state occupation of all modes during EIT cooling. The length of the cooling was [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Single Ca+ compensation voltage for different axial voltages. The compensation voltage minima depend on the axial trapping voltage. a) For the y direction the crossing point marks the spot of the smallest axial micromotion and the typical operation point. Diagonal beam 1 scales with 0.138(5)Uax + 157(4) and diagonal beam 2 scales with 0.217(2)Uax + 93.1(1.9). b) The compensation voltage in x direction is m… view at source ↗
Figure 10
Figure 10. Figure 10: Micromotion change when dc and rf quadrupole fields are not aligned. a) If a single ion is shifted in [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ca+/Al+ crystal compensation voltage for different axial voltages. a) The first diagonal direction has two different distinct compensation values depending on the calcium position ”left” or ”right”. This difference is not visible for the second diagonal direction. b) For the top direction the difference between the two directions is small [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of the compensation voltage Uy measured on Al+ and Ca+ for different positions. The error of the Al+ measurement is larger due to its reduced sensitivity. This shows that the compensation points are not distinguishable. zation of the lock. One solution is to minimize micromotion for one position with Ca+, followed by a forced swap of the ions. Then the Al+ would be at a compensated position. Ho… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the sideband micromotion method (blue) with the PMSS method (black). Both show the [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: PMSS measurement example. Resulting ion excitation when scanning the rf phase modulation of the [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Setup used for the phase modulation of the 729 nm laser. The red lines imply laser paths, while the black [PITH_FULL_IMAGE:figures/full_fig_p022_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Measurement of the magnetic field for the lock in April 2025. The upper plot shows the average magnetic [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Estimated ac-Stark shift of the 397 nm σ beam. The dashed line indicates the power used during the clock interrogation. Table VI. Source of the uncertainties for all cooling and repumping lasers involved. For all beams, we use multiple power measurements and fit the results to estimate the frequency shift at the power used during the experiment. This leads to an additional statistical extrapolation error.… view at source ↗
Figure 18
Figure 18. Figure 18: The light shift of the clock laser depends on the polarization. We want to drive the [PITH_FULL_IMAGE:figures/full_fig_p029_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Temperature measurement with the PT100 sensor on the trap’s sapphire discs. The blue line shows the [PITH_FULL_IMAGE:figures/full_fig_p031_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Frequency shift caused by the electric field of the trap. Since the electric field is different for the two-ion [PITH_FULL_IMAGE:figures/full_fig_p032_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Laser drift seen by the lock. The feedback enables us to calculate the drift of the laser without feedback. [PITH_FULL_IMAGE:figures/full_fig_p033_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Measurement scheme for the phase chirp caused by an AOM. [PITH_FULL_IMAGE:figures/full_fig_p034_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Measurement of the phase chirp of a Rabi clock cycle. Here, only the averaged data is displayed. The [PITH_FULL_IMAGE:figures/full_fig_p034_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Estimated pressure at the ion positions measured via position changes during the clock measurement due [PITH_FULL_IMAGE:figures/full_fig_p036_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Height determination of the experiment to the reference marker. GLM30 is a digital laser measure and [PITH_FULL_IMAGE:figures/full_fig_p038_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Comparison of absolute frequency measurements of the Al [PITH_FULL_IMAGE:figures/full_fig_p040_26.png] view at source ↗
read the original abstract

Advances in optical clocks motivate a redefinition of the second, requiring rigorous evaluations of systematic uncertainties and robust consistency among the clocks. Here, we report the full evaluation of the systematic frequency shifts of an $^{27}\mathrm{Al}^+$ single-ion clock, and the measurement of its absolute frequency and frequency ratio with a $^{87}$Sr optical lattice clock at PTB. The evaluated total systematic fractional frequency uncertainty is $1.6\times10^{-18}$, mainly limited by the accuracy of the relevant atomic coefficients and by background gas collisions. The absolute frequency of the clock has been measured to be $\nu_{\mathrm{Al}^+}=1 121 015 393 207 859.19(24)\,$Hz, obtained by comparison with two primary caesium fountain clocks at PTB. The frequency ratio between the Al and Sr optical clocks has been determined to be $\nu_{\mathrm{Al}^+}/\nu_{^{87}\mathrm{Sr}}=2.611 701 431 781 462 668(36)$, limited by the accuracy of the Sr clock. This ratio differs by $8.6\sigma$ and $1.2\sigma$ from the 2021 and 2025 frequency ratio published by the BACON collaboration, respectively. These results represent an important contribution toward a future redefinition of the second using optical clocks, and underscore the importance of independent measurements of clock-candidate frequency ratios across different institutions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reports a complete evaluation of systematic frequency shifts for a single-ion ^{27}Al^+ optical clock, yielding a total fractional uncertainty of 1.6×10^{-18} (dominated by uncertainties in atomic coefficients such as polarizabilities and quadrupole moments, plus background gas collisions). It also presents the absolute frequency measured against two PTB Cs fountain clocks and the frequency ratio with a ^{87}Sr lattice clock, including noted discrepancies with prior BACON collaboration results.

Significance. If the uncertainty budget holds, the work supplies an independent, high-precision data point for optical-clock frequency ratios and absolute frequencies. This directly supports the consistency checks required for a future redefinition of the second and underscores the value of cross-institution comparisons.

major comments (1)
  1. The abstract states that the total systematic uncertainty is limited by the accuracy of atomic coefficients, but the manuscript must explicitly show (in the systematic evaluation section) how literature uncertainties on polarizabilities, quadrupole moments, and related coefficients are propagated into each shift term and combined in quadrature with the experimental contributions; without this propagation the 1.6×10^{-18} claim cannot be verified as load-bearing.
minor comments (2)
  1. Clarify the data-exclusion criteria and averaging intervals used for the ratio and absolute-frequency measurements to allow independent assessment of statistical robustness.
  2. Add a brief table or paragraph comparing the new ratio value and its uncertainty directly with the 2021 and 2025 BACON values, including the exact σ calculation method.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the recommendation of minor revision. The single major comment is addressed point-by-point below; we will incorporate the requested clarification in the revised manuscript.

read point-by-point responses

  1. Referee: The abstract states that the total systematic uncertainty is limited by the accuracy of atomic coefficients, but the manuscript must explicitly show (in the systematic evaluation section) how literature uncertainties on polarizabilities, quadrupole moments, and related coefficients are propagated into each shift term and combined in quadrature with the experimental contributions; without this propagation the 1.6×10^{-18} claim cannot be verified as load-bearing.

    Authors: We agree that the propagation of literature uncertainties must be shown explicitly to allow independent verification of the total budget. In the revised manuscript we will add a new subsection (or expanded table) in the systematic evaluation section that lists, for each relevant shift (quadratic Stark, quadrupole, etc.), the literature value and its uncertainty, the propagation formula applied to the operating conditions, the resulting contribution to the fractional frequency shift, and the quadrature combination with all experimental uncertainties. This addition will make the 1.6×10^{-18} total fully traceable. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental comparisons are direct and self-contained

full rationale

The paper reports direct experimental measurements of the Al+ clock frequency against Cs fountains and the frequency ratio against an Sr lattice clock. The systematic uncertainty budget of 1.6e-18 is explicitly stated to be limited by external atomic coefficients (polarizabilities, quadrupole moments) and background gas collisions, without any internal derivation or fit that reduces to the same dataset by construction. No self-citation chains, ansatzes, or fitted inputs presented as predictions appear in the provided text. The central claims rest on laboratory comparisons and tabulated external coefficients, making the result independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard atomic-physics models for calculating frequency shifts and on the accuracy of previously measured atomic coefficients; no new entities or ad-hoc parameters are introduced in the abstract.

axioms (1)
  • domain assumption Standard models for electric quadrupole, magnetic dipole, and blackbody radiation shifts in trapped ions are sufficiently accurate for the stated uncertainty budget.
    Invoked when the paper states that the total systematic uncertainty is limited by the accuracy of the relevant atomic coefficients.

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Reference graph

Works this paper leans on

300 extracted references · 65 canonical work pages · 5 internal anchors

  1. [1]

    Klose, Joshua and Stahl, Kilian and Schwarz, Roman and Rahm, Johannes and Poudel, N and Weyers, Stefan and Benkler, Erik and D

  2. [2]

    (Middlebury, VT, US), Kaplan, Harvey B

    Monroe, Christopher (Ellicott City, US), Pagano, Guido (Washington, DC, US), Hess, Paul W. (Middlebury, VT, US), Kaplan, Harvey B. (College Park, MD, US), Tan, Wen Lin (College Park, MD, US), Richerme, Philip J. (Bloomington, IN, US),

  3. [3]

    and Chaitanya N., Apurv and Jabir, M

    Aadhi, A. and Chaitanya N., Apurv and Jabir, M. V. and Singh, R. P. and Samanta, G. K. , year = 2015, journal =. All-Periodically Poled, High-Power, Continuous-Wave, Single-Frequency Tunable

    2015

  4. [4]

    Blueprint for Fault-Tolerant Quantum Computation with Topological Qubit Arrays , author =. Phys. Rev. Res. , volume =

  5. [5]

    and Abadie, J

    Aasi, J. and Abadie, J. and Abbott, B. P. and Abbott, R. and Abbott, T. D. and Abernathy, M. R. and Adams, C. and Adams, T. and Addesso, P. and Adhikari, R. X. and Affeldt, C. and Aguiar, O. D. and Ajith, P. and Allen, B. and Ceron, E. Amador and Amariutei, D. and Anderson, S. B. and Anderson, W. G. and Arai, K. and Araya, M. C. and Arceneaux, C. and Ast,...

    work page doi:10.1038/nphoton.2013.177 2013

  6. [6]

    arXiv:1205.1362 , eprint =

    Single Ion Heat Engine with Maximum Efficiency at Maximum Power , author =. arXiv:1205.1362 , eprint =

    Pith/arXiv arXiv

  7. [7]

    Nature , volume =

    Observation of Constructive Interference at the Edge of Quantum Ergodicity , author =. Nature , volume =. doi:10.1038/s41586-025-09526-6 , copyright =

    work page doi:10.1038/s41586-025-09526-6

  8. [8]

    Compact Transportable

    Abbasov, Timur and Makarenko, Konstantin and Sherstov, Ivan and Axenov, Mikhail and Zalivako, Ilya and Semerikov, Ilya and Khabarova, Ksenia and Kolachevsky, Nikolay and Chepurov, Sergey and Taichenachev, Alexei and Bagaev, Sergey and Tausenev, Anton , year = 2020, journal =. Compact Transportable. 2010.15244 , primaryclass =

    arXiv 2020

  9. [9]

    and Zibrov, S

    Abbasov, T. and Zibrov, S. and Sherstov, I. , year = 2023, journal =. Surface-

    2023

  10. [10]

    ArXiv190611495 Phys

    Guidelines for Developing Optical Clocks with 10. ArXiv190611495 Phys. , eprint =

  11. [11]

    Abdeldayem, H. A. and Dowdye, E. and Canham, J. and Jaeger, T. , year = 2005, volume =. Contamination and Radiation Effects on Spaceflight Laser Systems , booktitle =

    2005

  12. [12]

    ArXiv161004927 Quant-Ph , eprint =

    Local Probe of Single Phonon Dynamics in Warm Ion Crystals , author =. ArXiv161004927 Quant-Ph , eprint =

  13. [13]

    and Walser, A

    Abdolvand, A. and Walser, A. M. and Ziemienczuk, M. and Nguyen, T. and Russell, P. Generation of a Phase-Locked. Opt. Lett. , volume =

  14. [14]

    and Argentin, C

    Abdoulanziz, A. and Argentin, C. and Laporta, V. and Chakrabarti, K. and Bultel, A. and Tennyson, J. and Schneider, I. F. and Mezei, J. Low-Energy Electron Impact Dissociative Recombination and Vibrational Transitions of. J. Appl. Phys. , volume =

  15. [15]

    Abe, Minori and Kajita, Masatoshi and Hada, Masahiko and Moriwaki, Yoshiki , year = 2010, journal =

    2010

  16. [16]

    Ab Initio Study on Potential Energy Curves of Electronic Ground and Excited States of

    Abe, Minori and Moriwaki, Yoshiki and Hada, Masahiko and Kajita, Masatoshi , year = 2012, journal =. Ab Initio Study on Potential Energy Curves of Electronic Ground and Excited States of

    2012

  17. [17]

    and Chattopadhyay, Swapan and Coleman, Jonathon and Curfman, Noah M

    Abe, Mahiro and Adamson, Philip and Borcean, Marcel and Bortoletto, Daniela and Bridges, Kieran and Carman, Samuel P. and Chattopadhyay, Swapan and Coleman, Jonathon and Curfman, Noah M. and DeRose, Kenneth and Deshpande, Tejas and Dimopoulos, Savas and Foot, Christopher J. and Frisch, Josef C. and Garber, Benjamin E. and Geer, Steve and Gibson, Valerie a...

  18. [18]

    and Gebbe, M

    Abend, S. and Gebbe, M. and Gersemann, M. and Ahlers, H. and M. Atom-. Phys. Rev. Lett. , volume =

  19. [19]

    Atomic Fountains and Optical Clocks at

    Abgrall, Michel and Chupin, Baptiste and De Sarlo, Luigi and Gu. Atomic Fountains and Optical Clocks at. Comptes Rendus Physique , series =

  20. [20]

    Coherent. Phys. Rev. Lett. , volume =. doi:10.1103/PhysRevLett.94.040405 , lccn =

    work page doi:10.1103/physrevlett.94.040405

  21. [21]

    Science , volume =

    Observation of Vortex Lattices in. Science , volume =

  22. [22]

    Nature , volume =

    Fault-Tolerant Operation of a Logical Qubit in a Diamond Quantum Processor , author =. Nature , volume =. doi:10.1038/s41586-022-04819-6 , copyright =

    work page doi:10.1038/s41586-022-04819-6

  23. [23]

    and Cornell, Eric A

    Abraham, Eric R.I. and Cornell, Eric A. , year = 1998, journal =. Teflon. doi:10.1364/AO.37.001762 , lccn =

    work page doi:10.1364/ao.37.001762 1998

  24. [24]

    Abraham, E. R. I. and McAlexander, W. I. and Gerton, J. M. and Hulet, R. G. and C. Triplet S-Wave Resonance in. Phys. Rev. A , volume =

  25. [25]

    and Lloyd, Seth , year = 1999, journal =

    Abrams, Daniel S. and Lloyd, Seth , year = 1999, journal =. Quantum

    1999

  26. [26]

    Andrew D

    Acampora, Giovanni and Ambainis, Andris and Ares, Natalia and Banchi, Leonardo and Bhardwaj, Pallavi and Binosi, Daniele and Briggs, G. Andrew D. and Calarco, Tommaso and Dunjko, Vedran and Eisert, Jens and Ezratty, Olivier and Erker, Paul and Fedele, Federico and. Quantum Computing and Artificial Intelligence: Status and Perspectives , shorttitle =. doi:...

    work page doi:10.48550/arxiv.2505.23860

  27. [27]

    Nature , volume =

    Quantum Error Correction below the Surface Code Threshold , author =. Nature , volume =. doi:10.1038/s41586-024-08449-y , copyright =

    work page doi:10.1038/s41586-024-08449-y

  28. [28]

    Nature , volume =

    Suppressing Quantum Errors by Scaling a Surface Code Logical Qubit , author =. Nature , volume =. doi:10.1038/s41586-022-05434-1 , copyright =

    work page doi:10.1038/s41586-022-05434-1

  29. [29]

    Achtenberg, Krzysztof and Miko. Low-. Electronics , volume =. doi:10.3390/electronics9081245 , copyright =

    work page doi:10.3390/electronics9081245

  30. [30]

    The Quantum Technologies Roadmap: A

    Ac. The Quantum Technologies Roadmap: A. New J. Phys. , volume =

  31. [31]

    Ackerman, Z. E. D. and Quevedo, A. Cadarso and Maran, Ilango and Gallagher, L. P. H. and Spreeuw, R. J. C. and Berengut, J. C. and Gerritsma, R. , year = 2026, number =. Long-Lived Metastable States in the 4f. doi:10.48550/arXiv.2603.04250 , archiveprefix =. 2603.04250 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2603.04250 2026

  32. [32]

    Detection and

    Acton, Mark , year = 2008, school =. Detection and

    2008

  33. [33]

    and Brickman, K.A

    Acton, M. and Brickman, K.A. and Haljan, P.C. and Lee, P.J. and Deslauriers, L. and Monroe, C. , year = 2006, journal =. Near-

    2006

  34. [34]

    Review of Scientific Instruments , volume =

    Low Noise Near-Concentric Optical Cavity Design , author =. Review of Scientific Instruments , volume =

  35. [35]

    Optical Atomic Clocks:

    Adam, David , year = 2003, journal =. Optical Atomic Clocks:

    2003

  36. [36]

    , year = 2021, journal =

    Adams, Austin and Pinto, Elton and Young, Jeffrey and Herold, Creston and McCaskey, Alex and Dumitrescu, Eugene and Conte, Thomas M. , year = 2021, journal =. Enabling a. 2111.00146 , primaryclass =

    arXiv 2021

  37. [37]

    Rydberg Atom Quantum Technologies , author =. J. Phys. B: At. Mol. Opt. Phys. , volume =

  38. [38]

    and Heckel, B.R

    Adelberger, E.G. and Heckel, B.R. and Nelson, A.E. , year = 2003, journal =. Tests of the

    2003

  39. [39]

    K , year = 2003, journal =

    Adhikari, S. K , year = 2003, journal =. Resonance in

    2003

  40. [40]

    and Fareed, Q

    Adivarahan, V. and Fareed, Q. and Srivastava, S. and Katona, T. and Gaevski, M. and Khan, A. , year = 2007, journal =. Robust 285 Nm Deep

    2007

  41. [41]

    Recoil Corrections in Highly Charged Ions , author =. Phys. Rev. A , volume =

  42. [42]

    Adler, F. and Mas. Mid-. Arxiv Prepr. ArXiv10070716 , eprint =

  43. [43]

    Observation of

    Adler, Daniel and Wei, David and Will, Melissa and Srakaew, Kritsana and Agrawal, Suchita and Weckesser, Pascal and Moessner, Roderich and Pollmann, Frank and Bloch, Immanuel and Zeiher, Johannes , year = 2024, journal =. Observation of. doi:10.1038/s41586-024-08188-0 , copyright =

    work page doi:10.1038/s41586-024-08188-0 2024

  44. [44]

    Phase-Locked Two-Branch Erbium-Doped Fiber Laser System for Long-Term Precision Measurements of Optical Frequencies , author =. Opt. Express , volume =

  45. [45]

    Atomic Clock Frequency Ratios with Fractional Uncertainty

    Aeppli, Alexander and. Atomic Clock Frequency Ratios with Fractional Uncertainty. doi:10.48550/arXiv.2512.21428 , archiveprefix =. 2512.21428 , primaryclass =

    work page doi:10.48550/arxiv.2512.21428

  46. [46]

    and Ye, Jun , year = 2024, journal =

    Aeppli, Alexander and Kim, Kyungtae and Warfield, William and Safronova, Marianna S. and Ye, Jun , year = 2024, journal =. Clock with 8 10

    2024

  47. [47]

    Clock with 8

    Aeppli, Alexander , year = 2025, address =. Clock with 8

    2025

  48. [48]

    and Kedar, Dhruv and He, Peiru and Rey, Ana Maria and Ye, Jun , year = 2022, journal =

    Aeppli, Alexander and Chu, Anjun and Bothwell, Tobias and Kennedy, Colin J. and Kedar, Dhruv and He, Peiru and Rey, Ana Maria and Ye, Jun , year = 2022, journal =. Hamiltonian Engineering of Spin-Orbit--Coupled Fermions in a

    2022

  49. [49]

    and Budker, D

    Afach, S. and Budker, D. and DeCamp, G. and Dumont, V. and Gruji. Characterization of the. ArXiv180709391 Phys. Physicsquant-Ph , eprint =

  50. [50]

    and Ayres, N

    Afach, S. and Ayres, N. J. and Baker, C. A. and Ban, G. and Bison, G. and Bodek, K. and Burghoff, M. and Geltenbort, P. and Green, K. and Griffith, W. C. and. A. ArXiv150904411 Hep-Ex Physicsphysics , eprint =

  51. [51]

    Search for Topological Defect Dark Matter with a Global Network of Optical Magnetometers , author =. Nat. Phys. , volume =. doi:10.1038/s41567-021-01393-y , copyright =

    work page doi:10.1038/s41567-021-01393-y

  52. [52]

    and Solyanik, Maria , year = 2018, journal =

    Afanasev, Andrei and Carlson, Carl E. and Solyanik, Maria , year = 2018, journal =. Atomic. 1801.03227 , primaryclass =

    Pith/arXiv arXiv 2018

  53. [53]

    and Ambar, O

    Afek, I. and Ambar, O. and Silberberg, Y. , year = 2010, journal =. High-

    2010

  54. [54]

    A Compact Laser Head with High-Frequency Stability for

    Affolderbach, Christoph and Mileti, Gaetano , year = 2005, journal =. A Compact Laser Head with High-Frequency Stability for

    2005

  55. [55]

    ArXiv200800035 Phys

    Phase-Coherent Sensing of the Center-of-Mass Motion of Trapped-Ion Crystals , author =. ArXiv200800035 Phys. , eprint =

  56. [56]

    Toward Improved Quantum Simulations and Sensing with Trapped Two-Dimensional Ion Crystals via Parametric Amplification , author =. Phys. Rev. A , volume =

  57. [57]

    and Halimi, Sami I

    Afzal, Francis O. and Halimi, Sami I. and Weiss, Sharon M. , year = 2018, journal =. Design Approach for Side-Coupled Photonic Crystal Nanobeams:. 1805.09438 , primaryclass =

    Pith/arXiv arXiv 2018

  58. [58]

    Agababaev, V. A. and Glazov, D. A. and Volotka, A. V. and Zinenko, D. V. and Shabaev, V. M. and Plunien, G. , year = 2019, journal =. G Factor of the [(1s). doi:10.1002/xrs.3074 , copyright =

    work page doi:10.1002/xrs.3074 2019

  59. [59]

    Agababaev, V. A. and Glazov, D. A. and Volotka, A. V. and Zinenko, D. V. and Shabaev, V. M. and Plunien, G. , year = 2018, journal =. Ground-State g Factor of Middle-. 1812.06429 , primaryclass =

    Pith/arXiv arXiv 2018

  60. [60]

    Agababaev, V. A. and Prokhorchuk, E. A. and Glazov, D. A. and Malyshev, A. V. and Shabaev, V. M. and Volotka, A. V. , year = 2025, number =. doi:10.48550/arXiv.2505.08929 , archiveprefix =. 2505.08929 , primaryclass =

    work page doi:10.48550/arxiv.2505.08929 2025

  61. [61]

    Agababaev, V. A. and Volchkova, A. M. and Varentsova, A. S. and Glazov, D. A. and Volotka, A. V. and Shabaev, V. M. and Plunien, G. , year = 2017, journal =. Quadratic

    2017

  62. [62]

    Atomic States with Spectroscopic Squeezing , author =. Phys. Rev. A , volume =

  63. [63]

    doi:10.48550/arXiv.2405.16101 , archiveprefix =

    Entanglement Generation in Weakly-Driven Arrays of Multilevel Atoms via Dipolar Interactions , author =. doi:10.48550/arXiv.2405.16101 , archiveprefix =. 2405.16101 , primaryclass =

    work page doi:10.48550/arxiv.2405.16101

  64. [64]

    Agarwal, G. S. , year = 1976, journal =. Exact

    1976

  65. [65]

    Quantum Statistical Theory of Optical-Resonance Phenomena in Fluctuating Laser Fields , author =. Phys. Rev. A , volume =

  66. [66]

    S , year = 2010, journal =

    Agarwal, G. S , year = 2010, journal =. Quantum. 1009.4449 , archiveprefix =

    Pith/arXiv arXiv 2010

  67. [67]

    and Rafailov, E

    Agate, B. and Rafailov, E. U. and Sibbett, W. and Saltiel, S. M. and Battle, P. and Fry, T. and Noonan, E. , year = 2003, journal =. Highly Efficient Blue-Light Generation from a Compact, Diode-Pumped Femtosecond Laser by Use of a Periodically Poled

    2003

  68. [68]

    and Bauswein, Andreas and Cella, Giancarlo and Clesse, Sebastian and Cruise, Adrian Michael and Domcke, Valerie and Figueroa, Daniel G

    Aggarwal, Nancy and Aguiar, Odylio D. and Bauswein, Andreas and Cella, Giancarlo and Clesse, Sebastian and Cruise, Adrian Michael and Domcke, Valerie and Figueroa, Daniel G. and Geraci, Andrew and Goryachev, Maxim and Grote, Hartmut and Hindmarsh, Mark and Muia, Francesco and Mukund, Nikhil and Ottaway, David and Peloso, Marco and Quevedo, Fernando and Ri...

  69. [69]

    M and Keenan, F

    Aggarwal, K. M and Keenan, F. P , year = 1998, journal =. Excitation Rate Coefficients for Fine-Structure Transitions in

    1998

  70. [70]

    Room-Temperature Optomechanical Squeezing , author =. Nat. Phys. , volume =. doi:10.1038/s41567-020-0877-x , copyright =

    work page doi:10.1038/s41567-020-0877-x

  71. [71]

    Review of Scientific Instruments , volume =

    A Supersonic Laser Ablation Beam Source with Narrow Velocity Spreads , author =. Review of Scientific Instruments , volume =

  72. [72]

    Nature , volume =

    Scaling and Networking a Modular Photonic Quantum Computer , author =. Nature , volume =. doi:10.1038/s41586-024-08406-9 , copyright =

    work page doi:10.1038/s41586-024-08406-9

  73. [73]

    Laser Cooling of a Magnetically Guided Ultracold Atom Beam , author =. New J. Phys. , volume =

  74. [74]

    Lightwave

    Agilent , year = 2000, number =. Lightwave

    2000

  75. [75]

    Aguilera, D. N. and Ahlers, H. and Battelier, B. and Bawamia, A. and Bertoldi, A. and Bondarescu, R. and Bongs, K. and Bouyer, P. and Braxmaier, C. and. Class. Quantum Grav. , volume =

  76. [76]

    Fully Robust Qubit in Atomic and Molecular Three-Level Systems , author =. New J. Phys. , volume =

  77. [77]

    and Drewsen, M

    Aharon, N. and Drewsen, M. and Retzker, A. , year = 2013, journal =. General

    2013

  78. [78]

    Robust Optical Clock Transitions in Trapped Ions Using Dynamical Decoupling , author =. New J. Phys. , volume =

  79. [79]

    Aharonian, F. A. , year = 2003, journal =

    2003

  80. [80]

    Aharonian, Felix and Akamatsu, Hiroki and Akimoto, Fumie and Allen, Steven W. and Anabuki, Naohisa and Angelini, Lorella and Arnaud, Keith and Audard, Marc and Awaki, Hisamitsu and Axelsson, Magnus and Bamba, Aya and Bautz, Marshall and Blandford, Roger and Brenneman, Laura and Brown, Gregory V. and Bulbul, Esra and Cackett, Edward and Chernyakova, Maria ...

    work page doi:10.1038/nature18627

Showing first 80 references.