  Engineering strong interactions between optical photons is a great challenge
for quantum science. Envisioned applications range from the realization of
photonic gates for quantum information processing to synthesis of photonic
quantum materials for investigation of strongly-correlated driven-dissipative
systems. Polaritonics, based on the strong coupling of photons to atomic or
electronic excitations in an optical resonator, has emerged as a promising
approach to implement those tasks. Recent experiments demonstrated the onset of
quantum correlations in the exciton-polariton system, showing that strong
polariton blockade could be achieved if interactions were an order of magnitude
stronger. Here, we report time resolved four-wave mixing experiments on a
two-dimensional electron system embedded in an optical cavity, demonstrating
that polariton-polariton interactions are strongly enhanced when the electrons
are initially in a fractional quantum Hall state. Our experiments indicate that
in addition to strong correlations in the electronic ground state,
exciton-electron interactions leading to the formation of polaron polaritons
play a key role in enhancing the nonlinear optical response. Besides potential
applications in realization of strongly interacting photonic systems, our
findings suggest that nonlinear optical measurements could provide information
about fractional quantum Hall states that is not accessible in linear optical
response.
