Non-Equilibrium Quantum Dynamics of Ultra-Cold Atomic Mixtures: the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons

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 in order to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and the efficiency of the method, we explore the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with vanishing intra-species interaction is 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 of the second species exhibit a bunching tendency, whose strength can be influenced by their coupling to the third species.