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Physical Review A

Multipole, nonlinear, and anharmonic uncertainties of clocks of Sr atoms in an optical lattice

Vitalii D Ovsiannikov, Vitalii G Pal'chikov, А. В. Тайченачев, Valeriy I. Yudin, Hidetoshi Katori

Published Jul 8, 2013• 32 citations
Publisher

Abstract

Magnetic-dipole, electric-quadrupole, and hyperpolarizability effects on clock energy levels are analyzed in detail for Sr atoms in Stark potentials of red-detuned and blue-detuned magic-wavelength optical lattices. A difference between ac Stark shifts in traveling and standing waves is determined numerically. Differences between magic wavelengths for atoms in traveling and standing waves are presented and strategies for minimizing uncertainties of the clock frequency are indicated explicitly. Significant suppression of hyperpolarizability effect is demonstrated analytically for a blue-detuned in comparison with a red-detuned lattice, thus enabling essential deepening of trap potentials, reducing tunneling between lattice wells and collision effects.

DOI
10.1103/physreva.88.013405

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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
Magnetic-dipole, electric-quadrupole, and hyperpolarizability effects on clock energy levels are analyzed in detail for Sr atoms in Stark potentials of red-detuned and blue-detuned magic-wavelength optical lattices. A difference between ac Stark shifts in traveling and standing waves is determined numerically. Differences between magic wavelengths for atoms in traveling and standing waves are presented and strategies for minimizing uncertainties of the clock frequency are indicated explicitly. Significant suppression of hyperpolarizability effect is demonstrated analytically for a blue-detuned in comparison with a red-detuned lattice, thus enabling essential deepening of trap potentials, reducing tunneling between lattice wells and collision effects.
The budget of uncertainties of a time-frequency standard on neutral atoms, trapped in an optical lattice with a “magic wavelength” (MWL), includes a number of shift and broadening corrections, coming from interaction of atoms with different fields of environment. The most important corrections are those arising from interaction with the field of lattice wave. The lattice field is essentially stronger than other fields and may introduce severe perturbations on the standard frequency, despite its tuning to the MWL, which was proposed to compensate these perturbations in a standing-wave lattice, ensuring rigorous equality of the working-level shifts, independently of the atomic motion and the laser intensity. The method of determining MWL, based on measuring the shift of the clock frequency in a weak field of a travelling wave accounts for the Stark shift of energy levels, but only linear in the laser intensity, with inclusion of all multipole-interaction terms.
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may alter the definition of the magic wavelength to minimize the uncertainty of optical lattice clocks. We show that the magic wavelength can be determined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves. Experimental prospects of such lattices used with a blue magic wavelength are discussed.
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may introduce atomic-motion dependent clock uncertainties in optical lattice clocks. We show that the magic wavelength can be defined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves by allowing a spatially constant light shift arising from the latter two interactions. Experimental prospects of such lattices used with a blue magic wavelength are discussed.
We investigated the properties of optical lattice clocks operated with a repulsive light-shift potential. The magic wavelength, where light-shift perturbation for the clock transition cancels, was experimentally determined to be 389.889(9) nm for 87Sr. The hyperpolarizability effects on the clock transition were investigated theoretically. With minimal trapping field perturbation provided by the blue-detuned lattice, the fractional uncertainty due to the hyperpolarizability effects was found to be 2x10;{-19} in the relevant clock transition.
Abstract The energy levels and electric dipole ( E 1 ) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic E 1 , magnetic dipole ( M 1 ) and electric quadrupole ( E 2 ) polarizabilities as well as the hyperpolarizabilities of the 2 s 2 1 S 0 and 2 s 2 p 3 P 0 states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of 2 s 2 1 S 0 → 2 s 2 p 3 P 0 clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.
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​.