Multipolar polarizabilities and hyperpolarizabilities in the Sr optical lattice clock

Abstract

We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar $M1$ and $E2$ atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We have developed an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows to effectively and accurately carry out complete summations over intermediate states. We applied our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carried out an accurate calculation of the multipolar polarizabilities for these states at the magic frequency. Understanding these Stark shifts in optical lattice clocks is crucial for further improvement of the clock accuracy.

arXiv comment5 pages

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• Engineering Quantum States of Matter for Atomic Clocks in Shallow Optical Lattices
• Observation of an Inner-Shell Orbital Clock Transition in Neutral Ytterbium Atoms
• Calculation of higher-order corrections to the light shift of the $5s^2{}^1{S}_0$--$5s5p{}^3{P}_0^o$ clock transition in Cd
• Modeling motional energy spectra and lattice light shifts in optical lattice clocks
• Dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr lattice clock
• Optical Telecommunications-Band Clock based on Neutral Titanium Atoms
• Measurement of a ${}^7$Li tune-out wavelength by phase-patterned atom interferometry
• Observation of effects due to an atom's electric quadrupole polarizability
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• Be optical lattice clocks with the fractional Stark shift up to the level of 10${}^{-19}$
• Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths
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