Ultracold atoms have openened up the way towards the study of seemingly exotic quantum systems, such as the one-dimensional (1D) Bose gas. This system has the intriguing feature that the bosons behave much like an ideal Fermi gas in the limit of hard-core repulsion (fermionization). This talk deals with the mechanism of the interaction crossover from an ideal Bose gas to the fermionization limit from a few-body perspective.
In the first part, the basic mechanism of this crossover is discussed for the ground state, with a special emphasis on the interplay between two-body interactions and the trapping potential. An extension to the case of attractive bosons and binary mixtures will be discussed. The second part is devoted to the impact of this crossover on the quantum dynamics, specifically the tunneling dynamics in a double-well trap. The dynamics changes over from Rabi oscillations to multi-band tunneling for increasing repulsion. The tunneling can be controlled by making the wells asymmetric.