  Quantum dynamics of impurities in a bath of bosons is a long-standing problem
of solid-state, plasma, and atomic physics. Recent experimental and theoretical
investigations with ultracold atoms focused on this problem, studying atomic
impurities immersed in a 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 made of few $^{41}$K atoms and a BEC
made of $^{87}$Rb atoms in a quasi one-dimensional configuration and under a
weak harmonic axial confinement. For small values of the interspecies
interaction strength (no matter the sign of it), we find that the impurity,
which starts from outside the BEC, simply oscillates back and forth the BEC
cloud, 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 interspecies interaction is attractive, a
local maximum (bright soliton) in the density of BEC occurs where the impurity
is trapped; instead, if the interspecies interaction is repulsive, the impurity
is not able to enter in the BEC cloud and the reflection coefficient is close
to one. On the other hand, if the initial displacement of the impurity is
increased, the impurity is able to penetrate in the cloud leading to the
appearance of a moving hole (dark soliton) in the BEC.
