  Topological field theories emerge at low energy in strongly-correlated
condensed matter systems and appear in the context of planar gravity. In
particular, the study of Chern-Simons terms gives rise to the concept of flux
attachment when the gauge field is coupled to matter, yielding flux-charge
composites. Here we investigate the generation of flux attachment in a
Bose-Einstein condensate in the presence of non-linear synthetic gauge
potentials. In doing so, we identify the U(1) Chern-Simons gauge field as a
singular density-dependent gauge potential, which in turn can be expressed as a
Berry connection. We envisage a proof-of-concept scheme where the artificial
gauge field is perturbatively induced by an effective light-matter detuning
created by interparticle interactions. At a mean field level, we recover the
action of a "charged" superfluid minimally coupled to both a background and a
Chern-Simons gauge field. Remarkably, a localised density perturbation in
combination with a non-linear gauge potential gives rise to an effective
composite boson model of fractional quantum Hall effect, displaying anyonic
vortices.
