Zeeman frequency shifts in an optical dipole trap used to search for an electric-dipole moment

We calculate the Zeeman frequency shifts due to interactions with the light in a far-off-resonance optical dipole trap. These shifts are important for potential use of such a trap to search for an atomic permanent electric-dipole moment (EDM). We present numerical results for Cs and Hg, as examples of paramagnetic and diamagnetic atoms. The vector and tensor light shifts are calculated for a large range of trap optical frequencies, for both red-detuned and blue-detuned traps. We also consider frequency shifts resulting from magnetic dipole and electric quadrupole transitions mixed in by a static electric field. These shifts are particularly important for EDM experiments since they are linear in the electric field. The Zeeman frequency shifts represent a substantial problem for EDM experiments in a dipole trap and must be controlled with care to achieve theoretical sensitivity.