  The quantum Rabi model describes the coupling of a two-state system to a
bosonic field mode. Recent theoretical work has pointed out that a generalized
periodic version of this model, which maps onto Hamiltonians applicable in
superconducting qubit settings, can be quantum simulated with cold trapped
atoms. Here, we experimentally demonstrate atomic dynamics predicted by the
periodic quantum Rabi model far in the deep strong coupling regime. The
two-state system is represented by two Bloch bands of cold atoms in an optical
lattice, and the bosonic mode by oscillations in a superimposed optical dipole
trap potential. The observed dynamics beyond the usual quantum Rabi physics
becomes relevant when the edge of the Brillouin zone is reached, and evidence
for collapse and revival of the initial state is revealed at extreme coupling
conditions.
