高维超冷玻色原子的平均场动力学：多组态方法面临的挑战
Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach
摘要：
探索维度对陷阱中相互作用玻色子的量子动力学（包括粒子关联）的影响是一项有趣但具有挑战性的任务。由于参与长度尺度的不同，三维短程相互作用的建模起着特殊的作用。我们回顾了后者的不同方法，并阐述了多构型计算策略有限范围的潜力是足够的，从而需要大网格来解决相关的长度尺度。这导致了计算上的挑战，其中还包括复杂性随原子数量的指数缩放。我们表明，最近开发的玻色子的从头算多层多分辨时间相关Hartee方法（ML-MCTDHB）[J. Chem. Phys. 139，134103（2013）]可以面对数值挑战，并在三维空间中提出ML-MCTDHB的有效数值实现，特别适合于描述细长陷阱的量子动力学。我们的方法的有益的缩放证明通过研究隧道动力学的玻色子系综在一个双井。比较三维与准一维的模拟，我们发现密度的维数诱导效应。此外，我们研究的交叉从弱横向约束，系统的平均场描述是足够的，对紧横向约束，粒子相关性和超越平均场效应是明显的。
英文摘要：
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.
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