## Lines of constant energy, with *z* versus

**Figure 2.** Lines of constant energy, with *z* versus . The initial conditions were *z*(0) = 0.5 and (0) = π. Figure (a) shows the numerical solutions to equations (20) and (21) with Λ = 2, while in (b) Λ = 0. The smallest to largest curves in each figure correspond to \gamma _1=\lbrace 0,\frac{1}{2},2\rbrace , respectively.

**Abstract**

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 analyse the phase-space trajectories of the system, and describe how the self-trapping is affected by the presence of an interacting gauge potential.