  Ultracold atomic gases have revolutionized the study of non-equilibrium
dynamics in quantum many-body systems. Many counterintuitive non-equilibrium
effects have been observed, such as suppressed thermalization in a
one-dimensional (1D) gas, the formation of repulsive self-bound dimers, and
identical behaviors for attractive and repulsive interactions. Here, we observe
the expansion of a bundle of ultracold 1D Bose gases in a flat-bottomed optical
lattice potential. By combining in situ measurements with photoassociation, we
follow the spatial dynamics of singly, doubly, and triply occupied lattice
sites. The system sheds interaction energy by dissolving some doublons and
triplons. Some singlons quantum distill out of the doublon center, while others
remain confined. Our Gutzwiller mean-field model captures these experimental
features in a physically clear way. These experiments might be used to study
thermalization in systems with particle losses or the evolution of quantum
entanglement, or if applied to fermions, to prepare very low entropy states.
