  Nonlinear optical responses provide a powerful way to understand the
microscopic interactions between laser fields and matter. They are critical for
plenty of applications, such as in lasers, integrated photonic circuits,
biosensing and medical tools. However, most materials exhibit weak optical
nonlinearities or long response times when they interact with intense optical
fields. Here, we strongly couple the exciton of organic molecules to an optical
mode of a Fabry-Perot cavity, and achieve an enhancement of the nonlinear
complex refractive index by two orders of magnitude compared with that of the
uncoupled condition. Moreover, the coupled system shows an ultrafast response
of ~120 fs that we extract from optical cross-correlation measurements. The
ultrafast and large enhancement of the nonlinar coefficients in this work paves
the way for exploring strong coupling effects on various third-order nonlinear
optical phenomena and for technological applications.
