Collision of impurities with Bose-Einstein condensates

Quantum dynamics of impurities in a bath of bosons is a long-standing problem in solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms have focused on this problem, studying atomic impurities immersed in an atomic Bose–Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano−Feshbach resonance technique. Here, we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity consisting of a few 41 K atoms and a BEC of 87 Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the inter-species interaction strength (regardless of its sign), we find that the impurity, which starts from outside the BEC, simply causes the BEC cloud to oscillate back and forth, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC, and strongly changes its amplitude of oscillation. In the strong interaction regime, if the inter-species interaction is attractive, a local maximum (bright soliton) in the BEC density occurs where the impurity is trapped; if, instead, the inter-species interaction is repulsive, the impurity is not able to enter the BEC cloud and the reflection coefficient is close to one. However, if the initial displacement of the impurity is increased, the impurity is able to penetrate the cloud, leading to the appearance of a moving hole (dark soliton) in the BEC