Engineering a topological gauge theory in an optically coupled 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 anyonic excitations emerge from 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, engineered quantum systems enable their direct implementation and provide a fertile playground to investigate their phenomenology without the need for strong interactions. In my talk, I will report on our recent realization of 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 favor of chiral matter interactions [1], which we engineer by synthesizing optically dressed atomic states with momentum-dependent scattering properties [2]. This allows us to reveal the key properties of the chiral BF theory: the formation of chiral solitons and the emergence of an electric field generated by the system itself [2]. Our results expand the scope of quantum simulation to topological gauge theories and pave the way towards implementing analogous gauge theories in higher dimensions.

[1] C. S. Chisholm, A. Frölian, E. Neri, R. Ramos, L. Tarruell, and A. Celi, Encoding a one-dimensional topological gauge theory in a Raman-coupled Bose-Einstein condensate, arXiv:2204.05386.

[2] A. Frölian, C. S. Chisholm, E. Neri, C. R. Cabrera, R. Ramos, A. Celi, and L. Tarruell, Realizing a 1D topological gauge theory in an optically dressed BEC, Nature 608, 293–297 (2022).