Interplay of asymmetry and fragmentation in the many-body tunneling dynamics of two-dimensional bosonic Josephson junctions

TL;DR

This study explores how asymmetry and fragmentation influence the many-body tunneling dynamics of two-dimensional bosonic Josephson junctions, revealing effects beyond mean-field predictions and highlighting the complex interplay of these factors.

Contribution

It introduces a detailed analysis of the interplay between asymmetry and fragmentation in 2D bosonic Josephson junctions, emphasizing many-body effects absent in mean-field models.

Findings

Transversal fragmentation is unaffected by asymmetry along the tunneling direction.

Asymmetry orthogonal to the junction reduces initial transversal fragmentation.

Asymmetry delays or accelerates the interference of fragmentations depending on its orientation.

Abstract

It is well known that the many-body tunneling of a bosonic condensate leads to (longitudinal) fragmentation along the tunneling direction. In this work, we prepare the initial ground state as a (transversely) fragmented system by introducing a barrier oriented orthogonally to the tunneling direction and allow it to tunnel through a two-dimensional longitudinally and transversely-asymmetric bosonic Josephson junctions. For a fixed barrier height, we find that the initial transversal fragmentation is essentially independent of the asymmetry along the tunneling direction but reduces when the asymmetry is oriented orthogonally to the junction. We investigate the interplay between the interference of fragmentations and asymmetry in the junction by analyzing the rate of density collapse in the survival probability, the uncertainty product, and the nontrivial dynamics of the occupation of the first excited orbital. The interference of fragmentations is quantified by the ratio between the reduction of transverse fragmentation and the development of longitudinal fragmentation. We show that asymmetry along the junction (orthogonal to the junction) delays (accelerates), compared to the symmetric potential, in obtaining the maximal interference of fragmentations. Notably, self-trapping opposes the interference, whereas a resonant tunneling condition enhances it. Overall, we demonstrate that the influence of asymmetry on the competition between longitudinal and transversal fragmentations, which together govern the macroscopic tunneling dynamics of interacting bosons, arises purely from the many-body effects and has no counterpart in the mean-field theory.