  The ground-state properties and excitation energies of a quantum emitter can
be modified in the ultrastrong coupling regime of cavity quantum
electrodynamics (QED) where the light-matter interaction strength becomes
comparable to the cavity resonance frequency. Recent studies have started to
explore the possibility of controlling an electronic material by embedding it
in a cavity that confines electromagnetic fields in deep subwavelength scales.
Currently, there is a strong interest in realizing ultrastrong-coupling cavity
QED in the terahertz (THz) part of the spectrum, since most of the elementary
excitations of quantum materials are in this frequency range. We propose and
discuss a promising platform to achieve this goal based on a two-dimensional
electronic material encapsulated by a planar cavity consisting of ultrathin
polar van der Waals crystals. As a concrete setup, we show that nanometer-thick
hexagonal boron nitride layers should allow one to reach the ultrastrong
coupling regime for single-electron cyclotron resonance in a bilayer graphene.
The proposed cavity platform can be realized by a wide variety of thin
dielectric materials with hyperbolic dispersions. Consequently, van der Waals
heterostructures hold the promise of becoming a versatile playground for
exploring the ultrastrong-coupling physics of cavity QED materials.
