Floquet Flux Attachment in Cold Atomic Systems

Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably, the fractional quantum Hall effect. The conventional picture states that strong interactions can have the net effect of binding flux quanta to underlying particles, leading to either composite fermions or bosons. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically driven (Floquet) system of two-component spins or hard-core bosons with nearest-neighbor interactions. We do so by demonstrating that such a system naturally realizes correlated hopping interactions that have a sharp connection with flux attachment. For a hard-core bosonic model on a bipartite square lattice, we find evidence that Floquet flux attachment stabilizes the bosonic integer quantum Hall state. We further explore the surrounding phase diagram as a function of two natural parameters and discover a surprisingly rich variety of phases, including a gapless phase best characterized as a composite Fermi liquid. Finally, we propose an experimental blueprint for realizing our protocol in ultra-cold atomic systems.