  Flux attachment provides a powerful conceptual framework for understanding
certain forms of topological order, including most notably the fractional
quantum Hall effect. 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 either spins or hard-core bosons. We
demonstrate that such a system naturally realizes correlated hopping
interactions and provides a sharp connection between such interactions and flux
attachment. Starting with a simple, nearest-neighbor, free boson model, we find
evidence -- from both a coupled wire analysis and large-scale density matrix
renormalization group simulations -- that Floquet flux attachment stabilizes
the bosonic integer quantum Hall state at $1/4$ filling (on a square lattice),
and the Halperin-221 fractional quantum Hall state at $1/6$ filling (on a
honeycomb lattice). At $1/2$ filling on the square lattice, time-reversal
symmetry is instead spontaneously broken and bosonic integer quantum Hall
states with opposite Hall conductances are degenerate. Finally, we propose an
optical-lattice-based implementation of our model on a square lattice and
discuss prospects for adiabatic preparation as well as effects of Floquet
heating.
