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 kandE 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 -> 4, 3 Cs transition frequency shift amounts to 7 mu Hz for a laser power of approximate to 1 kW at 877 nm, E=100 kV/cm and B greater than or similar to 0.5 G.