  We show that a nonlinear optical response associated with a resonant,
atomically thin material can be dramatically enhanced by placing it in front of
a partially reflecting mirror, rendering otherwise weakly nonlinear systems
suitable for experiments and applications involving quantum nonlinear optics.
Our approach exploits the nonlinear response of long-lived polariton resonances
that arise at particular distances between the material and the mirror. The
scheme is entirely based on free-space optics, eliminating the need for
cavities or complex nanophotonic structures. We analyze a specific
implementation based on exciton-polariton resonances in two-dimensional
semiconductors and discuss the role of imperfections and loss.
