Theoretical proposals to measure resonator-induced modifications of the electronic ground-state in doped quantum wells

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.