Andreev-reflection and Aharonov-Bohm dynamics in atomtronic circuits

We study the quantum transport through two specific atomtronic circuits: a Y-junction and a ring-shaped condensate pierced by an effective magnetic flux. Wedemonstrate that for bosons, the two circuits display Andreev-like reflections. For the Y-junction, the transport depends on the coupling strength of the Y-junction. For the ring-shaped condensate, the transport crucially depends on the particle statistics. For interacting bosons we find that the Aharonov-Bohm interference effect is absent. By breaking the translational invariance of the ring, the flux dependence can be restored. A complementary view of the problem is obtained through a specific non-equilibrium quench protocol. We find that the steady-state is independent of the flux, however the actual time-dynamics depends on the flux. The dynamics of the full closed system can be fitted with an approximated open system approach. For all the protocols we studied, we find striking differences in the dynamics of the Bose-Hubbard model and the Gross-Pitaevskii equation.