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

Recent interest in the physics of nonperturbative 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, despite being the object of many investigations, remain unobserved. In this paper, we investigate how virtual electronic excitations in quantum wells modify the ground-state charge distribution, and we propose two methods to measure such a cavity-induced perturbation. The first approach is based on spectroscopic mapping of the electronic population at a specific location in the quantum well using localized defect states. The second approach exploits instead the photonic equivalent of a Kelvin probe to measure the average charge 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.