  Interaction of dipolar polaritons can be efficiently tuned by means of a
shape resonance in their excitonic component. Provided the resonance width is
large, a squeezed population of strongly interacting polaritons may persist on
the repulsive side of the resonance. We derive an analytical expression for the
polariton coupling constant and show that it may have very large values in
typical experimental conditions. Our arguments provide a new direction for the
quest of interactions in quantum photonics.
