  Understanding the nature of confinement, as well as its relation with the
spontaneous breaking of chiral symmetry, remains one of the long-standing
questions in high-energy physics. The difficulty of this task stems from the
limitations of current analytical and numerical techniques to address
non-perturbative phenomena in non-Abelian gauge theories. In this work, we show
how similar phenomena emerge in simpler models, and how these can be further
investigated using state-of-the-art cold-atom quantum simulators. More
specifically, we introduce the rotor Jackiw-Rebbi model, a (1+1)-dimensional
quantum field theory where interactions between Dirac fermions are mediated by
quantum rotors. Starting from a mixture of ultracold atoms in an optical
lattice, we show how this quantum field theory emerges in the long-wavelength
limit. For a wide and experimentally-relevant parameter regime, the Dirac
fermions acquire a dynamical mass via the spontaneous breakdown of chiral
symmetry. Moreover, we study the effect of both quantum and thermal
fluctuations, which lead to the phenomenon of chiral symmetry restoration.
Finally, we uncover a confinement-deconfinement quantum phase transition, where
meson-like fermions fractionalise into quark-like quasi-particles bound to
topological solitons of the rotor field. The proliferation of these solitons at
finite chemical potentials again serves to restore the chiral symmetry,
yielding a clear analogy with the quark-gluon plasma in quantum chromodynamics,
where this symmetry coexists with the deconfined fractional charges. Our
results show how the interplay between these phenomena could be analyse in
realistic atomic experiments.
