1State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 2Graduate University of the Chinese Academy of Sciences, Beijing 100049 3Department of Physics, Henan Normal University, Xinxiang 453007
Abstract：The dynamic dipole polarizabilities for $1S$, $2S$ and $3S$ states of the hydrogen atom are calculated using the finite B-spline basis set method, and the magic wavelengths for $1S$–$2S$ and $1S$–$3S$ transitions are identified. In comparison of the solutions from the Schr?dinger and Dirac equations, the relativistic corrections on the magic wavelengths are of the order of $10^{-2}$ nm. The laser intensities for a 300-$E_{\rm r}$-deep optical trap and the heating rates at 514 and 1371 nm are estimated. The reliable prediction of the magic wavelengths would be helpful for the experimental design on the optical trapping of the hydrogen atoms, and in turn, it would be helpful to improve the accuracy of the measurements of the hydrogen $1S$–$2S$ and $1S$–$3S$ transitions.
Parthey C G, Matveev A, Alnis J, Bernhardt B, Beyer A, Holzwarth R, Maistrou A, Pohl R, Predehl K, Udem T, Wilken T, Kolachevsky N, Abgrall M, Rovera D, Salomon C, Laurent P and H?nsch T W 2011 Phys. Rev. Lett.107 203001
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Matveev A, Parthey C G, Predehl K, Alnis J, Beyer A, Holzwarth R, Udem T, Wilken T, Kolachevsky N, Abgrall M, Rovera D, Salomon C, Laurent P, Grosche G, Terra O, Legero T, Schnatz H, Weyers S, Altschul B and H?nsch T W 2013 Phys. Rev. Lett.110 230801
2016, Vol. 33 
