QED in graphene-hBN multilayer cavity

Subwavelength confinement of electromagnetic fields in artificial layered structures offers a powerful route to engineer tunable quantum light-matter interactions. We demonstrate that van der Waals multilayer cavities---composed of stacked graphene and hexagonal boron nitride(hBN)---enable unprecedented control over mode coupling and hybridization. By magnetically tuning graphene inter-Landau-level transitions into resonance with hBN phonon polaritons, we realize broadband, mode-selective strong coupling in the mid-infrared regime. Within our QED framework, we show that the vertical positioning and density of graphene layers dictate the hybridization strength, allowing systematic engineering of polaritonic bandgaps. Remarkably, we observe mode splitting exceeding the hBN Reststrahlen bandwidth, and find that increasing graphene layer density can drive the system into the ultrastrong-coupling regime at very large in-plane momenta. These results establish van der Waals multilayer cavities as a versatile platform for tunable multimode QED and reconfigurable quantum photonics in solid-state systems.