Domain formation and dynamics in a Bose-Einstein condensate with density-dependent gauge field

We investigate the equilibrium and dynamical properties of a Bose-Einstein condensate with a density-dependent gauge field. Based on Floquet engineering, we create a gauge field taking on one of two values, depending on whether the density exceeds a critical threshold. This allows a large change of the gauge field over a small range of the density, as well as formation of domains where atoms condense to different momenta. Our Floquet engineering scheme results in a low rate of loss and heating, enabling us to investigate the equilibrium and dynamical properties of the many-body system over hundreds of milliseconds. We observe the dependence of the condensate momentum on the local density in equilibrium, and find good agreement with theoretical predictions. We further study the dynamics of the domain walls in response to a change of the gauge field, and find a behavior consistent with energy relaxation.