%0 DATA
%A M, J Edmonds
%A M Valiente
%A P, Öhberg
%D 2013
%T Numerical solutions to equations (17) and (18)
%U https://iop.figshare.com/articles/_Numerical_solutions_to_equations_a_href_http_iopscience_iop_org_0953_4075_46_13_134013_article_jpb4/1012069
%R 10.6084/m9.figshare.1012069.v1
%2 https://iop.figshare.com/ndownloader/files/1479890
%K nonrigid pendulum
%K nonlinear Josephson equations
%K figure show
%K population oscillations
%X **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.