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We demonstrate theoretically the existence of a linear dc Stark shift of theindividual substates of an alkali atom in its ground state, dressed by acircularly polarized laser field. It arises from the electroweak nuclearanapole moment violating P but not T. It is characterized by the pseudoscalarequal to the mixed product formed with the photon angular momentum and staticelectric and magnetic fields. We derive the relevant left-right asymmetry withits complete signature in a field configuration selected for a precisionmeasurement with cold atom beams. The 3,3 to 4,3 Cs hyperfine-transitionfrequency shift amounts to 7 $\mu$Hz for a laser power of about 1 kW at 877 nm,E=100 kV/cm and B larger than 0.5 G.Comment: Article, 4 pages, 2 figure

Linear Stark Shift in Dressed Atoms as a Signal to Measure a Nuclear Anapole Moment with a Cold-Atom Fountain or Interferometer