Studies of 1D gases away from integrability*

We have studied atoms in optical lattices to address the fundamental question of what is needed for a many-body quantum system to approach a thermal distribution. Specifically, we prepare Rb atoms in an array of 1D tubes formed by a 2D optical lattice in so-called quantum Newton's cradle states,\footnote{Kinoshita \textit{et. al}, ``A quantum Newton's Cradle,'' Nature \textbf{440}, 900 (2006)} and then observe their time evolution. When the lattice is very deep, we can only set lower limits on the collision-dependent evolution of the momentum distribution. When the lattice is shallow enough that some atoms can populate the second vibrational band after a two-body collision, we find that the system thermalizes at a rate proportional to the inter-tube tunneling rate. For intermediate lattice depths, we observe collision-dependent evolution, but to final momentum distributions that seem to retain a memory of the initial state. Such partial thermalization is reminiscent of classical physics described by the KAM theorem.