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arXiv:1812.11815 · Physical Review Letters

Operational Magic Intensity for Sr Optical Lattice Clocks

Ichiro Ushijima, Masao Takamoto, Hidetoshi Katori

Published Dec 28, 2018• 112 citations
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Abstract

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.

DOI
10.1103/physrevlett.121.263202

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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.
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.
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.
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​.
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.
We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching 5×10(-17) after a 1 h integration time. We put the first experimental upper bound on the multipolar M1 and E2 interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the 10(-17) level, even for lattices as deep as 150 recoil energies.