  Artificial magnetic fields and spin-orbit couplings have been recently
generated in ultracold gases in view of realizing topological states of matter
and frustrated magnetism in a highly-controllable environment. Despite being
dynamically tunable, such artificial gauge fields are genuinely classical and
exhibit no back-action from the neutral particles. Here we go beyond this
paradigm, and demonstrate how quantized dynamical gauge fields can be created
in mixtures of ultracold atoms in optical lattices. Specifically, we propose a
protocol by which atoms of one species carry a magnetic flux felt by another
species, hence realizing an instance of flux-attachment. This is obtained by
combining coherent lattice modulation techniques with strong Hubbard
interactions. We demonstrate how this setting can be arranged so as to
implement lattice models displaying a local Z2 gauge symmetry, both in one and
two dimensions. We also provide a detailed analysis of a ladder toy model,
which features a global Z2 symmetry, and reveal the phase transitions that
occur both in the matter and gauge sectors. Mastering flux-attachment in
optical lattices envisages a new route towards the realization of
strongly-correlated systems with properties dictated by an interplay of
dynamical matter and gauge fields.
