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arXiv:2409.10782 · Physical Review Letters

Lattice Light Shift Evaluations in a Dual-Ensemble Yb Optical Lattice Clock

Tobias Bothwell, B. D. Hunt, Jacob L. Siegel, Youssef S. Hassan, Tanner Grogan, Takumi Kobayashi, Kurt Gibble, S. G. Porsev, Marianna S. Safronova, Roger C. Brown, K. Beloy, Andrew D. Ludlow

Published Jan 22, 2025• 12 citations
arXivHTMLPDF

Abstract

In state-of-the-art optical lattice clocks, beyond-electric-dipole polarizability terms lead to a breakdown of magic wavelength trapping. In this Letter, we report a novel approach to evaluate lattice light shifts, specifically addressing recent discrepancies in the atomic multipolarizability term between experimental techniques and theoretical calculations. We combine imaging and multi-ensemble techniques to evaluate lattice light shift atomic coefficients, leveraging comparisons in a dual-ensemble lattice clock to rapidly evaluate differential frequency shifts. Further, we demonstrate application of a running wave field to probe both the multipolarizability and hyperpolarizability coefficients, establishing a new technique for future lattice light shift evaluations.

DOI
10.1103/physrevlett.134.033201

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In state-of-the-art optical lattice clocks, beyond-electric-dipole polarizability terms lead to a breakdown of magic wavelength trapping. In this Letter, we report a novel approach to evaluate lattice light shifts, specifically addressing recent discrepancies in the atomic multipolarizability term between experimental techniques and theoretical calculations. We combine imaging and multi-ensemble techniques to evaluate lattice light shift atomic coefficients, leveraging comparisons in a dual-ensemble lattice clock to rapidly evaluate differential frequency shifts. Further, we demonstrate application of a running wave field to probe both the multipolarizability and hyperpolarizability coefficients, establishing a new technique for future lattice light shift evaluations.
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 an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).
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 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