  The regime of ultrastrong light-matter interaction has been investigated
theoretically and experimentally, using zero-dimensional electromagnetic
resonators coupled with an electronic transition between two confined states of
a semiconductor quantum well. We have measured a splitting between the coupled
modes that amounts to 48% of the energy transition, the highest ratio ever
observed in a light-matter coupled system. Our analysis, based on a microscopic
quantum theory, shows that the nonlinear polariton splitting, a signature of
this regime, is a dynamical effect arising from the self-interaction of the
collective electronic polarization with its own emitted field.
