  The quantum Rabi model describes the interaction between a two-level quantum
system and a single bosonic mode. We propose a method to perform a quantum
simulation of the quantum Rabi model introducing a novel implementation of the
two-level system, provided by the occupation of Bloch bands in the first
Brillouin zone by ultracold atoms in tailored optical lattices. The effective
qubit interacts with a quantum harmonic oscillator implemented in an optical
dipole trap. Our realistic proposal allows to experimentally investigate the
quantum Rabi model for extreme parameter regimes, which are not achievable with
natural light-matter interactions. Furthermore, we also identify a generalized
version of the quantum Rabi model in a periodic phase space.
