  The magnetotransport of a high-mobility two-dimensional electron gas coupled
to a hovering split-ring resonator with controllable distance is studied in the
quantum Hall regime. The measurements reveal an enhancement by more than a
factor 2 of the quantum Hall energy gaps at the fractional filling factors 4/3,
5/3, and 7/5, alongside a concurrent reduction in exchange splitting at odd
integer filling factors. Theoretically, we show the strength of both effects to
be quantitatively compatible with the emergence of an effective
electron-electron long-range attractive interaction mediated by the exchange of
virtual cavity photons in the presence of significant spatial gradients of the
cavity electric vacuum fields. These results unveil a compelling interplay
between cavity quantum electrodynamics and electronic correlations in
two-dimensional systems, with profound implications for the manipulation and
control of quantum phases in 2D materials.
