Impact of the range of the interaction on the quantum dynamics of a bosonic Josephson junction

The out-of-equilibrium quantum dynamics of a bosonic Josephson junction (BJJ) with long-range interaction is studied in real space by solving the time-dependent many-body Schr\"odinger equation numerically accurately using the multiconfigurational time-dependent Hartree method for bosons. Having the many-boson wave-function at hand we can examine the impact of the range of the interaction on the properties of the BJJ dynamics, viz. density oscillations and their collapse, self trapping, depletion and fragmentation, as well as the position variance, both at the mean-field and many-body level. Explicitly, the frequency of the density oscillations and the time required for their collapse, the value of fragmentation at the plateau, the maximal and the minimal values of the position variance in each cycle of oscillation and the overall pace of its growth are key to our study. We find competitive effect between the interaction and the confining trap. The presence of the tail part of the interaction basically enhances the effective repulsion as the range of the interaction is increased starting from a short, finite range. But as the range becomes comparable with the trap size, the system approaches a situation where all the atoms feel a constant potential and the impact of the tail on the dynamics diminishes. There is an optimal range of the interaction in which physical quantities of the junction are attaining their extreme values.Comment: Contribution to the Special Issue of Chemical Physics dedicated to Professor Hans-Dieter Meyer on the occasion of his 70th birthday; few typos correcte

Many-Body Quantum Dynamics of a Bosonic Josephson Junction with a Finite-Range Interaction

The out-of-equilibrium quantum dynamics of a Bose gas trapped in an asymmetric double well and interacting with a finite-range interaction has been studied in real space by solving the time-dependent many-body Schr\"odinger equation numerically accurately using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We have focused on the weakly interacting limit where the system is essentially condensed. We have examined the impact of the range of the interaction on the dynamics of the system, both at the mean-field and many-body levels. Explicitly, we have studied the maximal and the minimal values of the many-body position variance in each cycle of oscillation, and the overall pace of its growth. We find that the range of the interaction affects the dynamics of the system differently for the right well and the left well. We have also examined the infinite-particle limit and find that even there, the impact of the range of the interaction can only be described by a many-body theory such as MCTDHB