  Designer optical control of interactions in ultracold atomic gases has wide
application, from creating new quantum phases to modeling the physics of black
holes. We demonstrate spatial control of interactions in a two-component cloud
of $^6$Li fermions, using electromagnetically induced transparency (EIT) to
create a "sandwich" of resonantly and weakly interacting regions. Interaction
designs are imprinted on the trapped cloud by two laser beams and manipulated
with just MHz changes in the frequency of one beam. We employ radio-frequency
spectroscopy to measure the imprinted 1D spatial profiles of the local
mean-field interactions and to demonstrate that the tuning range of the
scattering length is the same for both optical and magnetic control. All of the
data are in excellent agreement with our continuum-dressed state theoretical
model of optical control, which includes both the spatial and momentum
dependence of the interactions.
