Dynamical phase diagram of a one-dimensional Bose gas in a box with a tunable weak link: From Bose-Josephson oscillations to shock waves

We study the dynamics of one-dimensional bosons trapped in a box potential in the presence of a barrier creating a tunable weak link, thus realizing a one-dimensional Bose-Josephson junction. By varying the initial population imbalance and the barrier height, we evidence different dynamical regimes. In particular, we show that at large barriers a two-mode model captures accurately the dynamics, while for low barriers the dynamics involves dispersive shock waves and solitons. We study a quench protocol that can be readily implemented in experiments and show that self-trapping resonances can occur. This phenomenon can be understood qualitatively within the two-mode model.