We consider an ultracold bosonic binary mixture confined in a one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled b
etween each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the inter-well population imbalance of each component and that between the two bosonic species. We study the Josephson oscillations of these spin-orbit coupled Bose-Einstein condensates by analyzing the interplay between the interatomic interactions and the spin-orbit coupling and the self-trapped dynamics of the inter-species imbalance. We show that the dynamics of this latter variable is crucially determined by the relationship between the spin-orbit coupling, the tunneling energy, and the interactions.
We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very different quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the speci
es. In the composite fermionization regime, where the interactions between both components are large, none of the species show large occupation of any natural orbital. Our results show that by increasing the interaction in one of the species, one can reach the phase-separated regime. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting component is displaced to the edges of the trap. The crossover is sharp, as observed in the in the energy and the in the largest occupation of a natural orbital of the weakly interacting species. Such a transition is a purely mesoscopic effect which disappears for large atom numbers.
Using calculations from first principles, we herein consider the bond made between thiolat e with a range of different Au clusters, with a particular focus on the spin moments inv olved in each case. For odd number of gold atoms, the clusters show a
spin moment of 1.~ $mu_B$. The variation of spin moment with particle size is particularly dramatic, with t he spin moment being zero for even numbers of gold atoms. This variation may be linked w ith changes in the odd-even oscillations that occur with the number of gold atoms, and is associated with the formation of a S-Au bond. This bond leads to the presence of an extra electron that is mainly sp in character in the gold part. Our results sugg est that any thiolate-induced magnetism that occurs in gold nanoparticles may be locali zed in a shell below the surface, and can be controlled by modifying the coverage of the thiolates.
