Tunable bandgap renormalization by nonlocal ultra-strong coupling in nanophotonics

In quantum optics, great effort is being invested in enhancing the interaction of quantum emitters with light. The different approaches include increasing the number of emitters, the laser intensity or the local photonic density of states at the location of an atom-like localized emitter. In contrast, solid-state extended emitters hold an unappreciated promise of vastly greater enhancements through their large number of vacant electronic valence states. However, the majority of valence states are considered optically inaccessible by a conduction electron. We show that, by interfacing three-dimensional (3D) solids with 2D materials, we can unlock the unoccupied valence states by nonlocal optical interactions that lead to ultra-strong coupling for each conduction electron. Consequently, nonlocal optical interactions fundamentally alter the role of the quantum vacuum in solids and create a new type of tunable mass renormalization and bandgap renormalization, which reach tens of millielectronvolts in the example we show. To present quantitative predictions, we develop a non-perturbative macroscopic quantum electrodynamic formalism that we demonstrate on a graphene-semiconductor-metal nanostructure. We find new effects, such as nonlocal Rabi oscillations and femtosecond-scale optical relaxation, overcoming all other solid relaxation mechanisms and fundamentally altering the role of optical interactions in solids. When interfacing a graphene layer with a thin solid emitter, the quantum plasmonic vacuum allows each solid electron to access all unoccupied valence states through the nonlocality of their light-matter interaction, creating ultra-strong coupling alongside mass and bandgap renormalization.