Non-equilibrium quantum dynamics of ultra-cold atomic mixtures: the multi-layer multi-configuration time-dependent Hartree method for bosons

Peter Schmelcher,Oriol Vendrell,Lushuai Cao,Sven Krönke

doi:10.1088/1367-2630/15/6/063018

Abstract

We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer feature allows for tailoring the wave function ansatz to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and efficiency of the method, we explored the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with vanishing intra-species interaction was weakly coupled. The population imbalances of the first two species can feature a temporal equilibration and their time evolution significantly depends on the coupling to the third species. Bosons of the first and second species exhibit a bunching tendency, whose strength can be influenced by their coupling to the third species.

Highlights

We develop and apply the multi-layer multi-configuration timedependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems
The multi-layer structure of our many-body wave function ansatz allows us to adapt our many-body basis to systemspecific inter- and intra-species correlations, which leads to a beneficial scaling
We have presented a novel ab initio method for simulating the non-equilibrium dynamics of mixtures of ultra-cold bosons

Summary

The multi-layer multi-configuration time-dependent Hartree boson method

Let us consider an ensemble of S bosonic species. The Hamiltonian of such a mixture with Nσ bosons of species σ = 1, . Hσ denotes the one-body Hamiltonian of the species σ containing a general speciesdependent trapping potential Uσ , Nσ. I =1 and Vσ and Wσσ refer to the intra-species interaction of species σ and to the inter-species interaction between σ and σ bosons, respectively: Vσ = gσ δ(xiσ. Note that the intra- and inter-species interaction strengths gσ , gσσ have to be properly renormalized with respect to their values in three-dimensional (3D) space as a consequence of dimensional reduction [7]. We remark that the Hamiltonian may be explicitly time dependent for studying driven systems

Wave function ansatz

Equations of motion

Application to correlated tunneling dynamics

Short-time tunneling dynamics

Long-time propagation and build-up of correlations

Findings

Conclusion and outlook