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Artificial magnetic fields and spin-orbit couplings have been recentlygenerated in ultracold gases in view of realizing topological states of matterand frustrated magnetism in a highly-controllable environment. Despite beingdynamically tunable, such artificial gauge fields are genuinely classical andexhibit no back-action from the neutral particles. Here we go beyond thisparadigm, and demonstrate how quantized dynamical gauge fields can be createdin mixtures of ultracold atoms in optical lattices. Specifically, we propose aprotocol by which atoms of one species carry a magnetic flux felt by anotherspecies, hence realizing an instance of flux-attachment. This is obtained bycombining coherent lattice modulation techniques with strong Hubbardinteractions. We demonstrate how this setting can be arranged so as toimplement lattice models displaying a local Z2 gauge symmetry, both in one andtwo dimensions. We also provide a detailed analysis of a ladder toy model,which features a global Z2 symmetry, and reveal the phase transitions thatoccur both in the matter and gauge sectors. Mastering flux-attachment inoptical lattices envisages a new route towards the realization ofstrongly-correlated systems with properties dictated by an interplay ofdynamical matter and gauge fields.

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories