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The magic wavelength for an optical lattice for hydrogen atoms that cancelsthe lowest order AC Stark shift of the 1S-2S transition is calculated to be 513nm. The magnitude of AC Stark shift $\Delta E=-1.19$ kHz/(10kW/cm$^2$) and theslope $d\Delta E/d\nu = -27.7$ Hz/(GHz $\cdot$ 10 kW/cm$^2$) at the magicwavelength suggests that a stable and narrow linewidth trapping laser isnecessary to achieve a deep enough optical lattice to confine hydrogen atoms ina way that gives a small enough light shift for the precision spectroscopy ofthe 1S-2S transition.

Magic Wavelength for Hydrogen 1S-2S Transition