On the Josephson effect in a Bose-Einstein condensate subject to a density dependent gauge potential

We investigate the coherent dynamics of a Bose-Einstein condensate in a double well, subject to a density dependent gauge potential. Further, we derive the nonlinear Josephson equations that allow us to understand the many-body system in terms of a classical Hamiltonian that describes the motion of a nonrigid pendulum with an initial angular offset. Finally we analyze the phase-space trajectories of the system, and describe how the self-trapping is affected by the presence of an interacting gauge potential.