  We present an optical approach to compensating for spatially varying ac-Stark
shifts that appear on atomic ensembles subject to strong optical control or
trapping fields. The introduction of an additional weak light field produces an
intentional perturbation between atomic states that is tuned to suppress the
influence of the strong field. The compensation field suppresses sensitivity in
one of the transition frequencies of the trapped atoms to both the atomic
distribution and motion. We demonstrate this technique in a cold rubidium
ensemble and show a reduction in inhomogeneous broadening in the trap. This
two-colour approach emulates the magic trapping approach that is used in modern
atomic lattice clocks but provides greater flexibility in choice of atomic
species, probe transition, and trap wavelength.
