The magic wavelength for an optical lattice for hydrogen atoms that cancels the lowest order ac Stark shift of the $1S\text{−}2S$ transition is calculated to be 513 nm. The magnitudes of the ac Stark shift $\mathrm{\Delta }E=-119$ $\text{Hz}/(\text{kW}/{\mathrm{cm}}^2)$ and the slope $d\mathrm{\Delta }E/d\nu =-2.77$ $\text{Hz}/(\text{GHz} \text{kW}/{\mathrm{cm}}^2)$ at the magic wavelength suggest that a stable and narrow-line-width trapping laser is necessary to achieve a deep enough optical lattice to confine hydrogen atoms in a way that gives a small enough light shift for the precision spectroscopy of the $1S\text{−}2S$ transition.

• Received 9 July 2015

DOI:https://doi.org/10.1103/PhysRevA.92.042507