Linear Stark shift in dressed atoms as a signal to measure a nuclear anapole moment with a cold-atom fountain or interferometer.

We demonstrate theoretically the existence of a linear dc Stark shift of the individual substates of an alkali atom in its ground state, dressed by a circularly polarized laser field. It arises from the electroweak nuclear anapole moment violating P but not T. It is characterized by the pseudoscalar {xi}k and E{center_dot}B involving the photon angular momentum and static electric and magnetic fields. We derive the relevant left-right asymmetry with its complete signature in a field configuration selected for a precision measurement with cold-atom beams. The 3, 3{yields}4, 3 Cs transition frequency shift amounts to 7 {mu}Hz for a laser power of {approx_equal}1 kW at 877 nm, E=100 kV/cm and B(greater-or-similar sign)0.5 G.