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Physical Review A

Magic-wave-induced S01−P03 transition in even isotopes of alkaline-earth-metal-like atoms

Vitaly D. Ovsiannikov, Vitaly G. Palchikov, А. В. Тайченачев, Valeriy I. Yudin, Hidetoshi Katori, Masao Takamoto

Published Feb 7, 2007• 47 citations
Publisher

Abstract

The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the $^{3}P_{1}$ state into the long-living metastable state $^{3}P_{0}$, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.

DOI
10.1103/physreva.75.020501

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The circular polarized laser beam of the magic'' wavelength may be used for mixing the $^{3}P_{1}$ state into the long-living metastable state $^{3}P_{0}$, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional state-mixing'' wave, including estimations of the magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
Magic-wave-induced 1S0−3P0^1S_0-^3P_01S0​−3P0​ transition in even isotopes of alkaline-earth-like atoms
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^3P_13P1​ state into the long-living metastable state 3P0^3P_03P0​, thus enabling the strictly forbidden 1S0^1S_01S0​−-−3P0^3P_03P0​ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional "state-mixing" wave, including estimations of the "magic" wavelengths, Rabi frequencies for the ''clock'' and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
The circular polarized laser beam of the “magic” wavelength used to produce an optical lattice for the time-frequency standard on neutral atoms may mix the 3P 1 state to the long-living metastable state 3P 0 thus providing significant enhancement of the strongly forbidden 1S 0 -3P 0 clock transition in even isotopes of alkaline-earth-like atoms. We present a detailed analysis of various factors influencing resolution and uncertainty for this kind of optical standard, including precise estimations of the “magic” wavelengths, transition matrix elements and field induced second- and fourth-order ac Stark shifts for the ground and metastable alkaline-earth-like atoms.
Magic wavelengths for laser trapping of boson isotopes of alkaline-earth metal atoms Sr, Ca, and Mg are investigated while considering terahertz clock transitions between the 3P0{}^{3}{P}_{0}3P0​, 3P1{}^{3}{P}_{1}3P1​, and 3P2{}^{3}{P}_{2}3P2​ metastable triplet states. Our calculation shows that magic wavelengths for laser trapping do exist. This result is important because those metastable states have already been used to make accurate clocks in the terahertz frequency domain. Detailed discussions for magic wavelengths for terahertz clock transitions are given in this article.
We present additional magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the clock transitions in the alkaline-earth-metal ions, considering circular polarized light, aside from our previously reported values [Kaur et al., Phys. Rev. A 92, 031402(R) (2015)] for linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities $[{\ensuremath{\alpha}}_{d}(\ensuremath{\omega})]$ of the atomic states associated with the clock transitions play major roles in the evaluation of these ${\ensuremath{\lambda}}_{\mathrm{magic}}$, hence facilitating choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The ${\ensuremath{\lambda}}_{\mathrm{magic}}$ values in these hyperfine transitions are estimated and found to be different from ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor parts of ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$. Importantly, we also present ${\ensuremath{\lambda}}_{\mathrm{magic}}$ values that depend only on the scalar component of ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$ for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present ${\ensuremath{\alpha}}_{d}(\ensuremath{\omega})$ values explicitly at 1064 nm for the atomic states associated with the clock transitions, which may be useful for creating high-field-seeking traps for the above ions using the Nd:YAG laser. The tune-out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.
We report direct single-laser excitation of the strictly forbidden (6s2)1S0 <--> (6s6p)3P0 clock transition in 174Yb atoms confined to a 1D optical lattice. A small (approximately 1.2 mT) static magnetic field was used to induce a nonzero electric dipole transition probability between the clock states at 578.42 nm. Narrow resonance linewidths of 20 Hz (FWHM) with high contrast were observed, demonstrating a resonance quality factor of 2.6 x 10(13). The previously unknown ac Stark shift-canceling (magic) wavelength was determined to be 759.35 +/- 0.02 nm. This method for using the metrologically superior even isotope can be easily implemented in current Yb and Sr lattice clocks and can create new clock possibilities in other alkaline-earth-like atoms such as Mg and Ca.
A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).