Atoms trapped in a red detuned retro-reflected Laguerre-Gaussian beam undergo orbital motion within rings whose centers are on the axis of the laser beam. We determine the wave functions, energies and degeneracies of such quantum rotors (QRs), and the microwave transitions between the energy levels are elucidated. We then show how such QR atoms can be used as high-accuracy rotation sensors when the rings are singly-occupied.
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