  Recent interest in the physics of non-perturbative light-matter coupling led
to the development of solid-state cavity quantum electrodynamics setups in
which the interaction energies are comparable with the bare ones. In such a
regime the ground state of the coupled system becomes interaction-dependent and
is predicted to contain a population of virtual excitations which,
notwithstanding having been object of many investigations, remain still
unobserved. In this paper we investigate how virtual electronic excitations in
quantum wells modify the ground-state charge distribution, and propose two
methods to measure such a cavity-induced perturbation. The first approach we
consider is based on spectroscopic mapping of the electronic population at a
specific location in the quantum well using localised defect states. The second
approach exploits instead the photonic equivalent of a Kelvin probe to measure
the average change distribution across the quantum well. We find both effects
observable with present-day or near-future technology. Our results thus provide
a route toward a demonstration of cavity-induced modulation of ground-state
electronic properties.
