Abstract
The magic wavelength for an optical lattice for hydrogen atoms that cancels the lowest order AC Stark shift of the 1S-2S transition is calculated to be 513 nm. The magnitude of AC Stark shift kHz/(10kW/cm) and the slope Hz/(GHz 10 kW/cm) at the magic wavelength suggests that a stable and narrow linewidth 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-2S transition.
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