Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach

TL;DR

This paper advances the simulation of ultra-cold bosonic atoms in higher dimensions by implementing an efficient multi-configurational approach, revealing dimensionality effects and correlation phenomena beyond mean-field approximations.

Contribution

It introduces a scalable 3D implementation of the ML-MCTDHB method, enabling detailed quantum dynamics studies of bosons in elongated traps with complex correlations.

Findings

Demonstrates the method's efficiency in 3D simulations

Reveals dimensionality-induced effects in density profiles

Studies the crossover from mean-field to correlated regimes

Abstract

Exploring the impact of dimensionality on the quantum dynamics of interacting bosons in traps including particle correlations is an interesting but challenging task. Due to the different participating length scales the modelling of the short-range interactions in three dimensions plays a special role. We review different approaches for the latter and elaborate that for multi-configurational computational strategies finite range potentials are adequate resulting in the need of large grids to resolve the relevant length scales. This results in computational challenges which include also the exponential scaling of complexity with the number of atoms. We show that the recently developed ab-initio Multi-Layer Multi-Configurational Time- Dependent Hartee method for Bosons (ML-MCTDHB) [J. Chem. Phys. 139, 134103 (2013)] can face both numerical challenges and present an efficient numerical implementation of ML-MCTDHB in three spatial dimensions, particularly suited to describe the quantum dynamics for elongated traps. The beneficial scaling of our approach is demonstrated by studying the tunnelling dynamics of bosonic ensembles in a double well. Comparing three-dimensional with quasi-one dimensional simulations, we find dimensionality-induced effects in the density. Furthermore, we study the crossover from weak transversal confinement, where a mean-field description of the system is sufficient, towards tight transversal confinement, where particle correlations and beyond mean-field effects are pronounced.