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Abstract
Using a simple semiclassical model, we explore ultrahigh-resolution optical two-photon spectroscopy of cold neutral atoms falling freely in a fountain. Considering atoms that interact with the same standing-wave laser field twice on their parabolic trajectories, and averaging over a Maxwellian velocity distribution, we predict a nearly Lorentzian line shape with just the natural linewidth. First-order Doppler shifts cancel even if the counterpropagating beams are slightly misaligned, and sub-Hertz resolution appears feasible with a fountain of modest dimensions.
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