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arXiv:1002.0119 · Physical Review A

Magic wavelengths for terahertz clock transitions

Xiaoji Zhou, Xia Xu, Xuzong Chen, Jingbiao Chen

Published Jan 25, 2010• 45 citations
arXivHTMLPDF

Abstract

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 ${}^{3}{P}_{0}$, ${}^{3}{P}_{1}$, and ${}^{3}{P}_{2}$ 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.

DOI
10.1103/physreva.81.012115

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arXiv:1703.08969•Physical Review A•Apr 6, 2017•17 citations
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.
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^{3}P_{1}3P1​ state into the long-living metastable state 3P0^{3}P_{0}3P0​, 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.
Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d 3 D 1 and 6s5d 3 D 2 are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.
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.
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.