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:2210.14727

Experimental determination of the E2-M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli, Christian Lisdat

Published Oct 26, 2022• 1 citation
arXivHTMLPDF

Abstract

To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few $10^{-18}$, as the resulting lattice light shift corrections deviate by up to $1 \times 10^{-17}$ from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our ${}^{87}\mathrm{Sr}$ lattice clock and find a value of $Δα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}$. This result is in very good agreement with the value reported by Ushijima et al.

DOI
10.48550/arxiv.2210.14727

Related papers

Experimental determination of the E2−M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli +1 more

State-of-the-art optical lattice clocks require careful characterization of systematic frequency shifts, which often needs to include contributions to the coupling of atoms to the trapping light field that are beyond the electric-dipole approximation. An experimental determination of the light-shift coefficient that accounts for electric-quadrupole and magnetic-dipole transitions for the clock transition in neutral strontium is reported on, addressing the substantial discrepancy between values detailed in previous works from theory and experiment.

Physical Review Research•Feb 7, 2023•9 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

Multipolar and higher-order lattice shifts in the Sr and Mg clocks

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

The progress in optical clock with uncertainty at a level of $10^{-18}$ requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Previous theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the 813 nm magic wavelength of the Sr clock differ substantially. We employ the sum-over-states method to calculate dynamic multipolar polarizabilities and hyperpolarizabilities for the Sr and Mg clocks. Our differential dynamic hyperpolarizability at the magic wavelength of 813.4280(5) nm for the Sr clock is $-2.09(43)\times10^{7}$ a.u., which agrees well with the recent theoretical and measurement results. Our differential multipolar polarizability of the Sr clock is $2.68(94)\times 10^{-5}$ a.u., which is consistent with the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)]. In addition, the lattice light shifts as the detuning and trap depth changed are studied in detail by using present multipolar polarizability and hyperpolarizability. It illustrates that for the Mg clock, there exists a distinctive operational lattice depth of $5.3(1)E_R$ that allows the total light shift reduced to less than $1\times 10^{-18}$ over the trap depth variation of $4.1E_R<U<6.4E_R$.

•Jun 5, 2019•0 citations

Calculation of higher-order corrections to the light shift of the 5s2 S01−5s5p P0o3 clock transition in Cd

S. G. Porsev, Marianna S. Safronova

In the recent work by Yamaguchi et al. [Phys. Rev. Lett. 123, 113201 (2019)] Cd was identified as an excellent candidate for a lattice clock. Here, we carried out computations needed for further clock development and made an assessment of the higher-order corrections to the light shift of the $5{s}^{2}$ $^{1}{S}_{0}\ensuremath{-}5s5p$ $^{3}{P}_{0}^{o}$ clock transition. We carried out calculations of the magnetic dipole and electric quadrupole polarizabilities and linear and circular hyperpolarizabilities of the $5{s}^{2}$ $^{1}{S}_{0}$ and $5s5p$ $^{3}{P}_{0}^{o}$ clock states at the magic wavelength and estimated uncertainties of these quantities. We also evaluated the second-order Zeeman clock transition frequency shift.

arXiv:2003.13855•Physical Review A•Jul 20, 2020•16 citations

Blackbody-radiation shift in the Sr optical atomic clock

Marianna S. Safronova, S. G. Porsev, Marianna S. Safronova +2 more

We evaluated the static and dynamic polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1$%$ uncertainty; $\ensuremath{-}$0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.

arXiv:1210.7272•Physical Review A•Jan 23, 2013•140 citations

Contributions of negative-energy states to the E2-M1 polarizability of the Sr clock

Wu, Fang-Fei, Ting-Yun Shi, Li-Yan Tang

With the improvement of high-precision optical clock, the higher-order multipolar interaction between atoms and light needs quantitative evaluation. However for the Sr clock, the differential dynamic E2-M1 polarizability at the magic wavelength has contradictions among available theoretical and experimental results. Recently, the new experimental measurement of S. Dörscher {\em et al.} [arXiv: 2210. 14727] is consistent with measurement of Ushijima {\em et al.}, which poses new challenges to theory and urgently calls for theoretical explanations. In present work, we investigate contributions of negative-energy states to the E2 and M1 polarizabilities. We find that for the M1 polarizability, the contribution from negative-energy states is crucial and dominant. Our new theoretical result for E2-M1 polarizability difference is $-7.74(3.92)\times 10^{-5}$ a.u., which is in good agreement with the recent experiment of S. Dörscher et al., so the inconsistency problem of E2-M1 polarizability in the Sr clock between theory and experiment is eliminated.

arXiv:2301.06740•Jan 17, 2023•0 citations
To operate an optical lattice clock at a fractional uncertainty below 10−1710^{-17}10−17, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states (5s5p) 3P0(5s5p)\,{}^{3}\mathrm{P}_{0}(5s5p)3P0​ and (5s2) 1S0(5s^2)\,{}^{1}\mathrm{S}_{0}(5s2)1S0​ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few 10−1810^{-18}10−18, as the resulting lattice light shift corrections deviate by up to 1×10−171 \times 10^{-17}1×10−17 from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our 87Sr{}^{87}\mathrm{Sr}87Sr lattice clock and find a value of Δαqm=−987−223+174  μHzΔα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}Δαqm​=−987−223+174​μHz. This result is in very good agreement with the value reported by Ushijima et al.
State-of-the-art optical lattice clocks require careful characterization of systematic frequency shifts, which often needs to include contributions to the coupling of atoms to the trapping light field that are beyond the electric-dipole approximation. An experimental determination of the light-shift coefficient that accounts for electric-quadrupole and magnetic-dipole transitions for the clock transition in neutral strontium is reported on, addressing the substantial discrepancy between values detailed in previous works from theory and experiment.
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 progress in optical clock with uncertainty at a level of 10−1810^{-18}10−18 requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Previous theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the 813 nm magic wavelength of the Sr clock differ substantially. We employ the sum-over-states method to calculate dynamic multipolar polarizabilities and hyperpolarizabilities for the Sr and Mg clocks. Our differential dynamic hyperpolarizability at the magic wavelength of 813.4280(5) nm for the Sr clock is −2.09(43)×107-2.09(43)\times10^{7}−2.09(43)×107 a.u., which agrees well with the recent theoretical and measurement results. Our differential multipolar polarizability of the Sr clock is 2.68(94)×10−52.68(94)\times 10^{-5}2.68(94)×10−5 a.u., which is consistent with the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)]. In addition, the lattice light shifts as the detuning and trap depth changed are studied in detail by using present multipolar polarizability and hyperpolarizability. It illustrates that for the Mg clock, there exists a distinctive operational lattice depth of 5.3(1)ER5.3(1)E_R5.3(1)ER​ that allows the total light shift reduced to less than 1×10−181\times 10^{-18}1×10−18 over the trap depth variation of 4.1ER<U<6.4ER4.1E_R<U<6.4E_R4.1ER​<U<6.4ER​.
In the recent work by Yamaguchi et al. [Phys. Rev. Lett. 123, 113201 (2019)] Cd was identified as an excellent candidate for a lattice clock. Here, we carried out computations needed for further clock development and made an assessment of the higher-order corrections to the light shift of the 5s25{s}^{2}5s2 $^{1}{S}_{0}\ensuremath{-}5s5p$ 3P0o^{3}{P}_{0}^{o}3P0o​ clock transition. We carried out calculations of the magnetic dipole and electric quadrupole polarizabilities and linear and circular hyperpolarizabilities of the 5s25{s}^{2}5s2 1S0^{1}{S}_{0}1S0​ and 5s5p5s5p5s5p 3P0o^{3}{P}_{0}^{o}3P0o​ clock states at the magic wavelength and estimated uncertainties of these quantities. We also evaluated the second-order Zeeman clock transition frequency shift.
We evaluated the static and dynamic polarizabilities of the 5s21S05{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}5s21S0​ and 5s5p3P0o5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}5s5p3P0o​ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1% uncertainty; $\ensuremath{-}0.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(70.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (70.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(7%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.
With the improvement of high-precision optical clock, the higher-order multipolar interaction between atoms and light needs quantitative evaluation. However for the Sr clock, the differential dynamic E2-M1 polarizability at the magic wavelength has contradictions among available theoretical and experimental results. Recently, the new experimental measurement of S. Dörscher {\em et al.} [arXiv: 2210. 14727] is consistent with measurement of Ushijima {\em et al.}, which poses new challenges to theory and urgently calls for theoretical explanations. In present work, we investigate contributions of negative-energy states to the E2 and M1 polarizabilities. We find that for the M1 polarizability, the contribution from negative-energy states is crucial and dominant. Our new theoretical result for E2-M1 polarizability difference is −7.74(3.92)×10−5-7.74(3.92)\times 10^{-5}−7.74(3.92)×10−5 a.u., which is in good agreement with the recent experiment of S. Dörscher et al., so the inconsistency problem of E2-M1 polarizability in the Sr clock between theory and experiment is eliminated.