  New functionalities in nonlinear optics will require systems with giant
optical nonlinearity as well as compatibility with photonic circuit fabrication
techniques. Here we introduce a new platform based on strong light-matter
coupling between waveguide photons and quantum-well excitons. On a
sub-millimeter length scale we generate sub-picosecond bright temporal solitons
at a pulse energy of only 0.5 pico-Joules. From this we deduce an unprecedented
nonlinear refractive index 3 orders of magnitude larger than in any other
ultrafast system. We study both temporal and spatio-temporal nonlinear effects
and for the first time observe dark-bright spatio-temporal solitons.
Theoretical modelling of soliton formation in the strongly coupled system
confirms the experimental observations. These results show the promise of our
system as a high speed, low power, integrated platform for physics and devices
based on strong interactions between photons.
