Hyperpolarizability and Operational Magic Wavelength in an Optical Lattice Clock
Open accessAbstract
Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an ^{171}Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the 10^{-18} level and beyond.
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The thermal shields facilitate characterisation of Stark effects from blackbody radiation and provide an in-situ Faraday enclosure shielding the atoms from static electric fields.
“This facilitates characterisation of a key systematic effect afflicting optical clocks, Stark effects from blackbody radiation bathing the ultracold atoms, and further provides an insitu Faraday enclosure shielding the atoms from static electric fields due to stray charges on the vacuum apparatus 24 .”
From Atomic clock performance enabling geodesy below the centimetre level (2018) · cites this paper as [24]
The Stark shift due to stray electric fields is consistent with zero at better than the 10^-19 level on both systems.
“By applying voltage to the windows of the thermal shield, the Stark shift due to stray electric fields is found to be consistent with zero at better than the 10 -19 level on both systems 24 .”
From Atomic clock performance enabling geodesy below the centimetre level (2018) · cites this paper as [24]
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Cites
Many-body physics with ultracold gases
Bloch, I., Dalibard, J., & Zwerger, W. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.885 · Cited by 8,114 · see citing works
Kimble, H. J. (2008) · Nature · doi:10.1038/nature07127 · Cited by 6,023 · see citing works
Optical Dipole Traps for Neutral Atoms
Grimm, R., Weidemüller, M., & Ovchinnikov, Y. B. (2000) · Advances in atomic, molecular, and optical physics · doi:10.1016/s1049-250x(08)60186-x · Cited by 1,550 · see citing works
An optical lattice clock with accuracy and stability at the 10−18 level
Bloom, B. J., Nicholson, T. L., Williams, J. R., Campbell, S. L., Bishof, M., Zhang, X., Zhang, W., Bromley, S. L., & Ye, J. (2014) · Nature · doi:10.1038/nature12941 · Cited by 1,073 · see citing works
Self-citationGeneration of ultrastable microwaves via optical frequency division
Fortier, T. M., Kirchner, M. S., Quinlan, F., Taylor, J. A., Bergquist, J., Rosenband, T., Lemke, N., Ludlow, A. D., Jiang, Y., Oates, C. W., et al. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.121 · Cited by 891 · see citing works
Self-citationTakamoto, M., Hong, F.-L., Higashi, R., & Katori, H. (2005) · Nature · doi:10.1038/nature03541 · Cited by 853 · see citing works
Chou, C. W., Hume, D. B., Rosenband, T., & Wineland, D. J. (2010) · Science · doi:10.1126/science.1192720 · Cited by 828 · see citing works
An Atomic Clock with 10 <sup>–18</sup> Instability
Hinkley, N., Sherman, J. A., Phillips, N. B., Schioppo, M., Lemke, N. D., Beloy, K., Pizzocaro, M., Oates, C. W., & Ludlow, A. D. (2013) · Science · doi:10.1126/science.1240420 · Cited by 817 · see citing works
Self-citationSystematic evaluation of an atomic clock at 2 × 10−18 total uncertainty
Nicholson, T. L., Campbell, S. L., Hutson, R. B., Marti, G. E., Bloom, B. J., McNally, R. L., Zhang, W., Barrett, M. D., Safronova, M. S., Strouse, G. F., et al. (2015) · Nature Communications · doi:10.1038/ncomms7896 · Cited by 780 · see citing works
Cryogenic optical lattice clocks
Ushijima, I., Takamoto, M., Das, M., Ohkubo, T., & Katori, H. (2015) · Nature Photonics · doi:10.1038/nphoton.2015.5 · Cited by 627 · see citing works
Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap
Katori, H., Takamoto, M., Pal’chikov, V. G., & Ovsiannikov, V. D. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.173005 · Cited by 576 · see citing works
Hunting for topological dark matter with atomic clocks
Derevianko, A., & Pospelov, M. (2014) · Nature Physics · doi:10.1038/nphys3137 · Cited by 522 · see citing works
Quantum State Engineering and Precision Metrology Using State-Insensitive Light Traps
Ye, J., Kimble, H. J., & Katori, H. (2008) · Science · doi:10.1126/science.1148259 · Cited by 413 · see citing works
Searching for dilaton dark matter with atomic clocks
Arvanitaki, A., Huang, J., & Van Tilburg, K. (2015) · Physical Review D · doi:10.1103/physrevd.91.015015 · Cited by 404 · see citing works
Ultrastable optical clock with two cold-atom ensembles
Schioppo, M., Brown, R. C., McGrew, W. F., Hinkley, N., Fasano, R. J., Beloy, K., Yoon, T. H., Milani, G., Nicolodi, D., Sherman, J. A., et al. (2017) · Nature Photonics · doi:10.1038/nphoton.2016.231 · Cited by 385 · see citing works
Self-citationHuntemann, N., Lipphardt, B., Tamm, C., Gerginov, V., Weyers, S., & Peik, E. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.210802 · Cited by 366 · see citing works
Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
Scazza, F., Hofrichter, C., Höfer, M., de Groot, P. C., Bloch, I., & Fölling, S. (2014) · Nature Physics · doi:10.1038/nphys3061 · Cited by 363 · see citing works
An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice
Danzl, J. G., Mark, M. J., Haller, E., et al. (2010) · Nature Physics · doi:10.1038/nphys1533 · Cited by 337 · see citing works
State-Insensitive Cooling and Trapping of Single Atoms in an Optical Cavity
McKeever, J., Buck, J. R., Boozer, A. D., Kuzmich, A., Nägerl, H., Stamper-Kurn, D., & Kimble, H. J. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.133602 · Cited by 332 · see citing works
Spin- 1/2 Optical Lattice Clock
Lemke, N., Ludlow, A. D., Barber, Z. W., Fortier, T. M., Diddams, S. A., Jiang, Y., Jefferts, S. R., Heavner, T. P., Parker, T. E., & Oates, C. W. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.063001 · Cited by 274 · see citing works
Self-citationExperimental realization of an optical second with strontium lattice clocks
Le Targat, R., Lorini, L., Le Coq, Y., Zawada, M., Guéna, J., Abgrall, M., Gurov, M., Rosenbusch, P., Rovera, D. G., Nagórny, B., et al. (2013) · Nature Communications · doi:10.1038/ncomms3109 · Cited by 250 · see citing works
Geopotential measurements with synchronously linked optical lattice clocks
Takano, T., Takamoto, M., Ushijima, I., Ohmae, N., Akatsuka, T., Yamaguchi, A., Kuroishi, Y., Munekane, H., Miyahara, B., & Katori, H. (2016) · Nature Photonics · doi:10.1038/nphoton.2016.159 · Cited by 245 · see citing works
Frequency ratio of Yb and Sr clocks with 5 × 10−17 uncertainty at 150 seconds averaging time
Nemitz, N., Ohkubo, T., Takamoto, M., Ushijima, I., Das, M., Ohmae, N., & Katori, H. (2016) · Nature Photonics · doi:10.1038/nphoton.2016.20 · Cited by 221 · see citing works
Fortier, T. M., Bartels, A., & Diddams, S. A. (2006) · Optics Letters · doi:10.1364/ol.31.001011 · Cited by 213 · see citing works
Self-citationA strontium lattice clock with 3 × 10<sup>−17</sup>inaccuracy and its frequency
Falke, S., Lemke, N., Grebing, C., Lipphardt, B., Weyers, S., Gerginov, V., Huntemann, N., Hagemann, C., Al-Masoudi, A., Häfner, S., et al. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/7/073023 · Cited by 182 · see citing works
Direct Observation of Coherent Interorbital Spin-Exchange Dynamics
Cappellini, G., Mancini, M., Pagano, G., Lombardi, P., Livi, L. F., de Cumis, M. S., Cancio, P., Pizzocaro, M., Calonico, D., Levi, F., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.120402 · Cited by 178 · see citing works
Towards a redefinition of the second based on optical atomic clocks
Riehle, F. (2015) · Comptes Rendus. Physique · doi:10.1016/j.crhy.2015.03.012 · Cited by 174 · see citing works
Rabi spectroscopy and excitation inhomogeneity in a one-dimensional optical lattice clock
Blatt, S., Thomsen, J. W., Campbell, G. K., Ludlow, A. D., Swallows, M. D., Martin, M. J., Boyd, M. M., & Ye, J. (2009) · Physical Review A · doi:10.1103/physreva.80.052703 · Cited by 166 · see citing works
Self-citationOptical Lattice Induced Light Shifts in an Yb Atomic Clock
Barber, Z. W., Stalnaker, J. E., Lemke, N., Poli, N., Oates, C. W., Fortier, T. M., Diddams, S. A., Hollberg, L. W., Hoyt, C., Тайченачев, А. В., et al. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.103002 · Cited by 160 · see citing works
Self-citationLattice-Induced Frequency Shifts in Sr Optical Lattice Clocks at the 10−17 Level
Westergaard, P. G., Lodewyck, J., Lorini, L., Lecallier, A., Burt, E. A., Zawada, M., Millo, J., & Lemonde, P. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.210801 · Cited by 137 · see citing works
Hyperpolarizability Effects in a Sr Optical Lattice Clock
Brusch, A., Targat, R. L., Baillard, X., Fouché, M., & Lemonde, P. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.103003 · Cited by 120 · see citing works
Experimental constraint on dark matter detection with optical atomic clocks
Wcisło, P., Morzyński, P., Bober, M., Cygan, A., Lisak, D., Ciuryło, R., & Zawada, M. (2016) · Nature Astronomy · doi:10.1038/s41550-016-0009 · Cited by 116 · see citing works
Quenched narrow-line laser cooling of 40Ca to near the photon recoil limit
Curtis, E. A., Oates, C. W., & Hollberg, L. (2001) · Physical Review A · doi:10.1103/physreva.64.031403 · Cited by 115 · see citing works
Optical lattice clock with atoms confined in a shallow trap
Lemonde, P., & Wolf, P. (2005) · Physical Review A · doi:10.1103/physreva.72.033409 · Cited by 114 · see citing works
All-optical production of a lithium quantum gas using narrow-line laser cooling
Duarte, P. M., Hart, R., Hitchcock, J. M., et al. (2011) · Physical Review A · doi:10.1103/physreva.84.061406 · Cited by 113 · see citing works
Entanglement of Light-Shift Compensated Atomic Spin Waves with Telecom Light
Dudin, Y. O., Radnaev, A. G., Zhao, R., Blumoff, J., Kennedy, T. A. B., & Kuzmich, A. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.260502 · Cited by 111 · see citing works
Einstein Gravity Explorer–a medium-class fundamental physics mission
Schiller, S., Tino, G. M., Gill, P. R., Salomon, C., Sterr, U., Peik, E., Nevsky, A. Y., Görlitz, A., Švehla, D., Ferrari, G., et al. (2008) · Experimental Astronomy · doi:10.1007/s10686-008-9126-5 · Cited by 110 · see citing works
Dynamic polarizabilities and related properties of clock states of the ytterbium atom
Dzuba, V. A., & Derevianko, A. (2010) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/43/7/074011 · Cited by 109 · see citing works
Constraining new physics models with isotope shift spectroscopy
Frugiuele, C., Fuchs, E., Pérez, G., et al. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.015011 · Cited by 89 · see citing works
Comparing a mercury optical lattice clock with microwave and optical frequency standards
Tyumenev, R., Favier, M., Bilicki, S., Bookjans, E., Targat, R. L., Lodewyck, J., Nicolodi, D., Coq, Y. L., Abgrall, M., Guéna, J., et al. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/11/113002 · Cited by 85 · see citing works
Self-citationStrategies for reducing the light shift in atomic clocks
Katori, H., Ovsiannikov, V. D., Marmo, S. I., & Palchikov, V. G. (2015) · Physical Review A · doi:10.1103/physreva.91.052503 · Cited by 74 · see citing works
Magic Wavelength to Make Optical Lattice Clocks Insensitive to Atomic Motion
Katori, H., Hashiguchi, K., Il’inova, E. Y., & Ovsiannikov, V. D. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.153004 · Cited by 67 · see citing works
Experimental observation of magic-wavelength behavior of Rb87 atoms in an optical lattice
Lundblad, N. E., Schlosser, M., & Porto, J. V. (2010) · Physical Review A · doi:10.1103/physreva.81.031611 · Cited by 65 · see citing works
Kulosa, A. P., Fim, D., Zipfel, K., Rühmann, S., Sauer, S., Jha, N., Gibble, K., Ertmer, W. A., Rasel, E. M., Safronova, M. S., et al. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.240801 · Cited by 65 · see citing works
Yang, J., He, X., Guo, R., Xu, P., Wang, K., Sheng, C., Liu, M., Wang, J., Derevianko, A., & Zhan, M. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.123201 · Cited by 62 · see citing works
Pizzocaro, M., Thoumany, P., Rauf, B., Bregolin, F., Milani, G., Clivati, C., Costanzo, G. A., Levi, F., & Calonico, D. (2017) · Metrologia · doi:10.1088/1681-7575/aa4e62 · Cited by 61 · see citing works
Self-citationТайченачев, А. В., Yudin, V. I., Ovsiannikov, V. D., Pal'chikov, V. G., & Oates, C. W. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.193601 · Cited by 56 · see citing works
Continuous-wave, single-frequency 229 nm laser source for laser cooling of cadmium atoms
Kaneda, Y., Yarborough, J. M., Merzlyak, Y., et al. (2016) · Optics Letters · doi:10.1364/ol.41.000705 · Cited by 46 · see citing works
Shi, C., Robyr, J.-L., Eismann, U., Zawada, M., Lorini, L., Le Targat, R., & Lodewyck, J. (2015) · Physical Review A · doi:10.1103/physreva.92.012516 · Cited by 37 · see citing works
Demonstration of a 1-W injection-locked continuous-wave titanium:sapphire laser
Cummings, E. A., Hicken, M., & Bergeson, S. (2002) · Applied Optics · doi:10.1364/ao.41.007583 · Cited by 32 · see citing works
Multipole, nonlinear, and anharmonic uncertainties of clocks of Sr atoms in an optical lattice
Ovsiannikov, V. D., Pal'chikov, V. G., Тайченачев, А. В., Yudin, V. I., & Katori, H. (2013) · Physical Review A · doi:10.1103/physreva.88.013405 · Cited by 32 · see citing works
Magic wavelengths for the 5 s – 18 s transition in rubidium
Goldschmidt, E. A., Norris, D. G., Koller, S., et al. (2015) · Physical Review A · doi:10.1103/physreva.91.032518 · Cited by 26 · see citing works
First Global Telescope Opens an Eye on the Cold Universe
Normile, D., & Clery, D. (2011) · Science · doi:10.1126/science.333.6051.1820 · Cited by 14 · see citing works
Measurement of gravitational time delay using drag-free spacecraft and an optical clock
Ashby, N., Bender, P. L., Hall, J. L., et al. (2009) · Proceedings of the International Astronomical Union · doi:10.1017/s1743921309990718 · Cited by 10 · see citing works
2024 European Frequency and Time Forum (EFTF)
(2024) · doi:10.1109/eftf61992.2024 · Cited by 6 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [57]C. Shi, J.-L. Robyr, U. Eismann, M. Zawada, L. Lorini, R. Le Targat, and J. Lodewyck, Phys. Rev. A 92 , 012516 (2015), URL http://link.aps.org/doi/10. 1103/PhysRevA.92.012516 .
- [58]A. P. Kulosa, D. Fim, K. H. Zipfel, S. R¨ uhmann, S. Sauer, N. Jha, K. Gibble, W. Ertmer, E. M. Rasel, M. S. Safronova, et al., Phys. Rev. Lett. 115 , 240801 (2015), URL https://link.aps.org/doi/10. 1103/PhysRevLett.115.240801 .
- [59]R. Tyumenev, M. Favier, S. Bilicki, E. Bookjans, R. L. Targat, J. Lodewyck, D. Nicolodi, Y. L. Coq, M. Abgrall, J. Guna, et al., New Journal of Physics 18 , 113002 (2016), URL http://stacks.iop.org/1367-2630/18/i= 11/a=113002 .
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Self-citation
- Authors
- 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., & Ludlow, A. D.
- Affiliations
- National Institute of Standards and Technology (US)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2017-12-19
- Volume
- 119
- Issue
- 25
- Pages
- 253001-253001
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2743882218
- Cited by
- 101
- References
- 55
- Citations by year
- 2026: 5 · 2025: 16 · 2024: 14 · 2023: 11 · 2022: 12 · 2021: 8 · 2020: 9 · 2019: 9 · 2018: 16 · 2017: 1
- FWCI
- 4.70
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- PORTO@Iris (submittedVersion, other-oa)
- PORTO Publications Open Repository TOrino (Politecnico di Torino) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- National Aeronautics and Space Administration
- Defense Advanced Research Projects Agency
- National Academy of Sciences
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Subatomic Physics Research
- Keywords
- optical lattice clock, hyperpolarizability, 171Yb, atomic temperature, systematic frequency shifts, clock accuracy
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