  We develop a theoretical model for the interaction strength between a pair of
exciton-polaritons with finite and parallel static electric-dipole moments. In
stark contrast to simple perturbative arguments predicting the interaction to
be reduced due to the hybridisation with cavity photons, we find that the
strong coupling to a cavity mode leads to a drastic enhancement of the
polariton interactions as compared to bare excitons. This enhancement is caused
by the small polariton mass due to its photonic component, which increases the
kinetic cost associated with minimising the dipole-dipole repulsion.
Microscopic numerical calculations for one-dimensional geometries show that the
interaction strength for the lower polariton branch is maximal when the exciton
and the cavity mode are close to resonance, and can easily exceed
state-of-the-art cavity decay rates for realistic confinement lengths, thus
entering the polariton blockade regime. Analytical extension of our results to
two-dimensional polariton systems highlight dipolar polaritons as a most
promising solid-state platform to realize strongly interacting photonic
systems.
