## Numerical solutions to equations (17) and (18)

**Figure 1.** Numerical solutions to equations (17) and (18). The population |*c _{l}*|

^{2}, |

*c*|

_{r}^{2}and ∑

_{i}|

*c*|

_{i}^{2}are given by the blue dashed line, solid red line and dashed black lines, respectively. (a) and (c) show the population oscillations for 2

*U*/

*J*= 10 and Γ

_{1}/

*J*= 1, the insets in each figure show the current

*J*(

*t*) as a function of time. Both (a) and (b) have the initial conditions c_{l/r}(t=0)=1/\sqrt{2}. (b) and (d) are plotted for 2

*U*/

*J*= 1 and Γ

_{1}/

*J*= 5. (c) and (d) have the initial conditions c_{l}(t=0)={\rm e}^{{\rm i}\pi /2}/\sqrt{2} and c_{r}(t=0)=1/\sqrt{2}. The units of time are /

*J*.

**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.