High-resolution spectroscopy of the 1S-2Stransition of atomic hydrogen and deuterium

Two-photon spectroscopy of the hydrogen 1S-2S transition in a cold atomic beam has reached a resolution {Δ}{ν}/{ν} of 1 part in 10¹¹ in hydrogen and 7 parts in 10¹² in deuterium. The hydrogen and deuterium 1S-2S transition frequencies have been determined with a precision of 1 part in 10¹¹. This leads to an accurate value for the Rydberg constant, while the 1S Lamb shift and the isotope shift are determined with order of magnitude improvements over previous measurements. We describe in detail the 1S-2S spectrometer, calculate the line shape of the resonance, and compare it to the experimental data.