Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1708.08829 · Physical Review Letters

Hyperpolarizability and Operational Magic Wavelength in an Optical Lattice Clock

Roger C. Brown, Nate Phillips, K. Beloy, William F. McGrew, M. Schioppo, Robert Fasano, Gianmaria Milani, Xiaogang Zhang, N. Hinkley, Holly Leopardi, Tai Hyun Yoon, Daniele Nicolodi, Tara M. Fortier, Andrew D. Ludlow

Published Dec 19, 2017• 101 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.119.253001

Related papers

Improving lattice-light-shift uncertainty of an 171Yb optical clock with optimized cooling and trapping lasers

Chengquan Peng, Tao Zhang, Changyue Sun +7 more

Atoms confined in the optical lattice can be interrogated with Doppler- and recoil-free operation. However, if not properly controlled, the optical lattice may limit clock accuracy. To improve the lattice-light-shift uncertainty, the cooling and trapping lasers' frequency stability is optimized, and the atom's signal stability is enhanced. A ring-cavity Ti:sapphire laser is locked to the optical frequency comb, which is referenced to a 578 nm ultra-stable laser, and the beat note's stability is on the order of 10−16. Using a 10 cm Fabry–Pérot cavity referenced to the Ti:sapphire laser, the optical frequency stability is transferred to the 399 nm cooling laser, creating favorable conditions for evaluating the lattice-light-shift accurately. We reevaluate lattice-light-shift in our 171Yb optical lattice clock with an uncertainty of 8.1 × 10−18, which is an order lower than our previous result, and the magic frequency is determined to be 394 798 266.6(1.3) MHz.

Applied Physics Letters•Sep 9, 2024•2 citations

Magic-intensity trapping of the Mg lattice clock with light shift suppressed below 10−19

Fang-Fei Wu, Yong-Bo Tang, Ting-Yun Shi +1 more

Progress in atomic optical clocks with total uncertainty of ${10}^{\ensuremath{-}18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of $5.33(2){E}_{R}$ (${E}_{R}$ is the lattice photon recoil energy) that reduces the total light shift below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ over $14%$ of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.

arXiv:1909.07692•Physical Review A•May 7, 2020•7 citations

Operational Magic Intensity for Sr Optical Lattice Clocks

Ichiro Ushijima, Masao Takamoto, Hidetoshi Katori

We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.

arXiv:1812.11815•Physical Review Letters•Dec 28, 2018•112 citations

Hyperpolarizability effects and accuracy evaluation of a 87Sr optical lattice clock

Rodolphe Le Targat, Anders Brusch, Xavier Baillard +4 more

The authors report the observation of the hyperpolarizability frequency shift due to the trapping field in a87Sr optical lattice clock. The authors show that at the magic wavelength of the lattice, where the first order term cancels, this higher order shift will not constitute a limitation to the fractional accuracy of the clock down to the 10-18level. This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm2and by a specific study of the effect of the two two-photon transitions near the magic wavelength. The authors also report an accurate frequency measurement of the clock transition. The frequency is determined to be v1S0-3P0= 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•Jun 1, 2006•1 citation

Characterization and Suppression of Background Light Shifts in an Optical Lattice Clock

Robert Fasano, Yun-Jhih Chen, William F. McGrew +3 more

Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancelation at the ten parts per billion level. Theory and empirical measurements can be used at varying levels of precision to determine the magic wavelength where shift cancelation occurs. However, lasers exhibit background spectra from amplified spontaneous emission or other lasing modes that can easily contaminate measurement of the magic wavelength and its reproducibility in other experiments or conditions. Indeed, residual light shifts from laser background have plagued optical lattice clock measurements for years. In this work, we develop a simple theoretical model allowing prediction of light shifts from measured background spectra. We demonstrate good agreement between this model and measurements of the background light shift from an amplified diode laser in a Yb optical lattice clock. Additionally, we model and experimentally characterize the filtering effect of a volume Bragg grating bandpass filter, demonstrating that application of the filter can reduce background light shifts from amplified spontaneous emission well below the ${10}^{\ensuremath{-}18}$ fractional clock frequency level. This demonstration is corroborated by direct clock comparisons between a filtered amplified diode laser and a filtered titanium:sapphire laser.

arXiv:2103.12052•Physical Review Applied•Apr 8, 2021•23 citations

Hyperpolarizability Effects in a Sr Optical Lattice Clock

Anders Brusch, Rodolphe Le Targat, Xavier Baillard +2 more

We report the observation of a higher-order frequency shift due to the trapping field in a (87)Sr optical lattice clock. We show that, at the magic wavelength of the lattice, where the first-order term cancels, the higher-order shift will not constitute a limitation to the fractional accuracy of the clock at a level of 10(-18). This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm(2) and by a specific study of the effect of the two two-photon transitions near the magic wavelength.

arXiv:physics/0512201•Physical Review Letters•Mar 16, 2006•120 citations
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.
Atoms confined in the optical lattice can be interrogated with Doppler- and recoil-free operation. However, if not properly controlled, the optical lattice may limit clock accuracy. To improve the lattice-light-shift uncertainty, the cooling and trapping lasers' frequency stability is optimized, and the atom's signal stability is enhanced. A ring-cavity Ti:sapphire laser is locked to the optical frequency comb, which is referenced to a 578 nm ultra-stable laser, and the beat note's stability is on the order of 10−16. Using a 10 cm Fabry–Pérot cavity referenced to the Ti:sapphire laser, the optical frequency stability is transferred to the 399 nm cooling laser, creating favorable conditions for evaluating the lattice-light-shift accurately. We reevaluate lattice-light-shift in our 171Yb optical lattice clock with an uncertainty of 8.1 × 10−18, which is an order lower than our previous result, and the magic frequency is determined to be 394 798 266.6(1.3) MHz.
Progress in atomic optical clocks with total uncertainty of ${10}^{\ensuremath{-}18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of 5.33(2)ER5.33(2){E}_{R}5.33(2)ER​ (ER{E}_{R}ER​ is the lattice photon recoil energy) that reduces the total light shift below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ over 1414%14 of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.
We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.
The authors report the observation of the hyperpolarizability frequency shift due to the trapping field in a87Sr optical lattice clock. The authors show that at the magic wavelength of the lattice, where the first order term cancels, this higher order shift will not constitute a limitation to the fractional accuracy of the clock down to the 10-18level. This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm2and by a specific study of the effect of the two two-photon transitions near the magic wavelength. The authors also report an accurate frequency measurement of the clock transition. The frequency is determined to be v1S0-3P0= 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancelation at the ten parts per billion level. Theory and empirical measurements can be used at varying levels of precision to determine the magic wavelength where shift cancelation occurs. However, lasers exhibit background spectra from amplified spontaneous emission or other lasing modes that can easily contaminate measurement of the magic wavelength and its reproducibility in other experiments or conditions. Indeed, residual light shifts from laser background have plagued optical lattice clock measurements for years. In this work, we develop a simple theoretical model allowing prediction of light shifts from measured background spectra. We demonstrate good agreement between this model and measurements of the background light shift from an amplified diode laser in a Yb optical lattice clock. Additionally, we model and experimentally characterize the filtering effect of a volume Bragg grating bandpass filter, demonstrating that application of the filter can reduce background light shifts from amplified spontaneous emission well below the ${10}^{\ensuremath{-}18}$ fractional clock frequency level. This demonstration is corroborated by direct clock comparisons between a filtered amplified diode laser and a filtered titanium:sapphire laser.
We report the observation of a higher-order frequency shift due to the trapping field in a (87)Sr optical lattice clock. We show that, at the magic wavelength of the lattice, where the first-order term cancels, the higher-order shift will not constitute a limitation to the fractional accuracy of the clock at a level of 10(-18). This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm(2) and by a specific study of the effect of the two two-photon transitions near the magic wavelength.