Magic Wavelengths for the 1S–2S and 1S–3S Transitions in Hydrogen Atoms

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.