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Physical Review A

Dynamic Stark shift of the 7 Li( 2s→3s ) transition

Li-Yan Tang, M. W. J. Bromley, Z.-C. Yan, J. Mitroy

Published Mar 11, 2013• 14 citations
Publisher

Abstract

The dynamic dipole polarizabilities for the $3s$ state of the Li atom are computed using Hylleraas and semiempirical approaches. This enables the calculation of the ${}^{7}$Li($2s\ensuremath{\rightarrow}3s$) Stark shift at photon wavelengths of 610.5 nm and 735.1 nm. They are calculated to be 834.7(5) and $\ensuremath{-}686.7(25)$ ${a}_{0}^{3}$, respectively. The first two tune-out frequencies for the ${}^{7}$Li($2s$) ground state are determined to be $670.971\phantom{\rule{0.16em}{0ex}}626(1)$ nm and $324.192(2)$ nm, respectively.

DOI
10.1103/physreva.87.032507

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The dynamic dipole polarizabilities for the 3s3s3s state of the Li atom are computed using Hylleraas and semiempirical approaches. This enables the calculation of the 7{}^{7}7Li(2s\ensuremath→3s2s\ensuremath{\rightarrow}3s2s\ensuremath→3s) Stark shift at photon wavelengths of 610.5 nm and 735.1 nm. They are calculated to be 834.7(5) and \ensuremath−686.7(25)\ensuremath{-}686.7(25)\ensuremath−686.7(25) a03{a}_{0}^{3}a03​, respectively. The first two tune-out frequencies for the 7{}^{7}7Li(2s2s2s) ground state are determined to be 670.971626(1)670.971\phantom{\rule{0.16em}{0ex}}626(1)670.971626(1) nm and 324.192(2)324.192(2)324.192(2) nm, respectively.
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Configuration interaction calculations are performed to determine the dipole polarizabilities and tune-out wavelengths for the 23S12{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}23S1​ state in Li+{\mathrm{Li}}^{+}Li+ ion. The finite nuclear mass correction is given by including the mass shift operator in the Dirac-Coulomb-Breit Hamiltonian directly, while the QED correction to dynamic dipole polarizabilities is evaluated by using the perturbation theory. The tune-out wavelengths for the 23S1(MJ=0)2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=0)23S1​(MJ​=0) and $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ states are 159.620 55(6) nm and 159.631 14(6) nm, respectively. And the QED correction for 159 nm tune-out wavelength is 43 ppm. In addition, we obtain the static dipole polarizability for the $2{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}\phantom{\rule{0.28em}{0ex}}({M}_{J}=\ifmmode\pm\else\textpm\fi{}1)$ state to be 46.857 03(4) a.u., in which the contribution from QED is 70 ppm. The 159 nm tune-out wavelength and the static dipole polarizability of 23S12{\phantom{\rule{0.28em}{0ex}}}^{3}{S}_{1}23S1​ state might provide a test of atomic structure theory.
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Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the 2s2s2s-2p2p2p and 2s2s2s-3p3p3p transitions in lithium. The nsnsns and npnpnp atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between 6{}^{6}6Li and 7{}^{7}7Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the 2s2s2s, 2p2p2p, 3s3s3s, 3p3p3p, and 3d3d3d levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv 2s2s2s-3p3p3p transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].
Recently, we studied the magic wavelength for the atomic hydrogen $1S\text{\ensuremath{-}}2S$ transition [A. Kawasaki, Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this paper, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. The magic wavelength, at which the lowest-order ac Stark shifts of the 1S1S1S and 2S2S2S states are equal, is found to be 514.6 nm. The ac Stark shift at the magic wavelength is $\ensuremath{-}221.6\phantom{\rule{0.28em}{0ex}}\mathrm{Hz}/(\mathrm{kW}/{\mathrm{cm}}^{2})$, and the slope of the ac Stark shift at the magic wavelength under a change of the driving laser frequency is $\ensuremath{-}0.2157\phantom{\rule{0.28em}{0ex}}\mathrm{Hz}/[\mathrm{GHz}\phantom{\rule{0.28em}{0ex}}(\mathrm{kW}/{\mathrm{cm}}^{2})]$.