Time-varying metasurfaces are emerging as a powerful instrument for the
dynamical control of the electromagnetic properties of a propagating wave. Here
we demonstrate an efficient time-varying metasurface based on plasmonic
nano-antennas strongly coupled to an epsilon-near-zero (ENZ) deeply
sub-wavelength film. The plasmonic resonance of the metal resonators strongly
interacts with the optical ENZ modes, providing a Rabi level spitting of ~30%.
Optical pumping at frequency {\omega} induces a nonlinear polarisation
oscillating at 2{\omega} responsible for an efficient generation of a phase
conjugate and a negative refracted beam with a conversion efficiency that is
more than four orders of magnitude greater compared to the bare ENZ film. The
introduction of a strongly coupled plasmonic system therefore provides a simple
and effective route towards the implementation of ENZ physics at the nanoscale