Abstract
We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprised of two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fails when the graphene sheet is heavily doped, i.e. when the Landau level spectrum of 2D massless Dirac fermions is approximately harmonic. In this case we `integrate out' the Landau levels in valence band and obtain an effective Hamiltonian for the entire stack of Landau levels in conduction band, as dressed by strong light-matter interactions.
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