Density-and-phase domain walls in a condensate with dynamical gauge potential

We show how one can generate domain walls that separate high- and low-density regions with opposite momenta in the ground state of a harmonically trapped Bose-Einstein condensate using a density-dependent gauge potential. Within a Gross-Pitaevskii framework, we elucidate the distinct roles of vector and scalar potentials and how they lead to synthetic electromagnetic fields that are localized at the domain wall. In particular, the kinetic energy cost of a steep density gradient is compensated by an electrostatic field that pushes particles away from a special value of density. We show numerically in one dimension that such a domain wall is more prominent for repulsive contact interactions, and becomes metastable at strong electric fields through a first-order phase transition that ends at a critical point as the field is reduced. We also provide simple variational that reproduce this metastability. Our findings build on recent experimental developments and may be realized with cold atoms in a shaken optical lattice, providing insights into collective phenomena arising from dynamical gauge fields.