2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134097It is shown that fermionic polar molecules or atoms in a bilayer optical lattice can undergo the transition to a state with circulating currents, which spontaneously breaks the time reversal symmetry. Estimates of relevant temperature scales are given and experimental signatures of the circulating current phase are identified. Related phenomena in bosonic and spin systems with ring exchange are discussed.final published versionOther Condensed MatterAtomic PhysicsQuantum Physicstext