Correlated dynamics of ultracold bosonic atoms in three dimensions : Facing the challenge with a multi-configurational approach

Sven Kr onke, Johannes Knörzer, Peter Schmelcher

Valentin Bolsinger, Sven Krönke, Peter Schmelcher

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 for large grids to resolve the relevant length scales. This results in computational challenges, which include 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) (2013 J. Chem. Phys. 139 134103 ) 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.

Laurent Sanchez-Palencia

L. Cao, V. Bolsinger, S. I. Mistakidis +4 more

We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of a mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species correlations. The versatility and efficiency of ML-MCTDHX are demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi types. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e., it is suppressed in the mean-field approximation.

Sven Krönke, Johannes Knörzer, Peter Schmelcher

We explore the correlated quantum dynamics of a single atom, regarded as an open system, with a spatio-temporally localized coupling to a finite bosonic environment. The single atom, initially prepared in a coherent state of low energy, oscillates in a one-dimensional harmonic trap and thereby periodically penetrates an interacting ensemble of N A bosons held in a displaced trap. We show that the inter-species energy transfer accelerates with increasing N A and becomes less complete at the same time. System-environment correlations prove to be significant except for times when the excess energy distribution among the subsystems is highly imbalanced. These correlations result in incoherent energy transfer processes, which accelerate the early energy donation of the single atom and stochastically favour certain energy transfer channels, depending on the instantaneous direction of transfer. Concerning the subsystem states, the energy transfer is mediated by non-coherent states of the single atom and manifests itself in singlet and doublet excitations in the finite bosonic environment. These comprehensive insights into the non-equilibrium quantum dynamics of an open system are gained by ab initio simulations of the total system with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons.

Roberto Onofrio, Luca Salasnich