Coupling of longitudinal and transversal fragmentations in the tunneling dynamics of Bose-Einstein condensates*

We propose a set-up to investigate tunneling dynamics of interacting bosons in the presence of coupling of longitudinal fragmentation, developed during the quantum dynamics, and transversal fragmentation, produced by the geometry of the trap. We find and explain how the coupling of fragmentations speeds up the collapse of density

oscillations and slows down the revival process by analyzing the survival probability along the junction, fluctuations of particle positions across the junction, and the occupancy of the lowest single-particle states. The coupling is manifested by the interference mechanism  which is always accompanied by a non-trivial transition from loss of coherence to build up of coherence in the first excited single-particle state. Moreover, it is found that a fully fragmented state significantly accelerates the revival process compared to the conventional Bose-Einstein condensate. We show that the interference of longitudinal and transversal fragmentations establishes new rules for macroscopic tunneling phenomena.