Realising a one-dimensional topological gauge theory in an optically dressed Bose-Einstein condensate

Topological gauge theories describe the low energy properties of certain strongly correlated quantum systems through effective weakly interacting models. A prime example is the Chern-Simons theory of fractional quantum Hall states, where the emergence of anyonic excitations is explained by the coupling between weakly interacting matter particles and a density-dependent gauge field. While in traditional solid-state platforms such gauge theories are only convenient theoretical constructions, experimental atomic systems enable their direct implementation and are expected to provide a fertile playground to investigate their phenomenology without the need for strong interactions. In my talk, I will report on the first quantum simulation of a topological gauge theory by realising a one-dimensional reduction of the Chern-Simons theory (the chiral BF theory) in a Bose-Einstein condensate. Using the local conservation laws of the theory, we eliminate the gauge degrees of freedom in favour of chiral matter interactions, which we engineer by synthesising optically dressed atomic states with momentum-dependent scattering properties. We explore the key properties of the chiral BF theory: the formation of chiral solitons - self-bound states of the matter field that only exist for one propagation direction - and the emergence of an electric field generated by the system itself. Our results expand the scope of quantum simulation to topological gauge theories and pave the way towards implementing analogous field theories in higher dimensions.