Exceptionally Slow Relaxation from Micro-canonical to Canonical Ensembles in Quasi-one-dimensional Quantum Gases

Integrability in one dimension prevents quantum thermalization and gives rise to rich many-body phenomena described by generalized hydrodynamics, which have been extensively studied over the past two decades using cold atoms in optically confined tubes. However, experimental work to date has focused primarily on low-energy states. Here, we report the experimental observation and theoretical understanding of near-integrable effects on thermalization in highly excited states. We design a protocol to prepare atoms within a high-energy window by combining a harmonic trap and a weak optical lattice: a Bose-Einstein condensate is initially prepared away from the trap center via Wannier-Stark localization and subsequently emits atoms into a selected energy window of highly excited states via Landau-Zener tunneling. By reconstructing the Wigner functions from the density distribution using a machine learning algorithm, we find that it takes an exceptionally long time, up to several seconds, for these atoms to gradually thermalize from an approximately microcanonical ensemble toward a canonical ensemble. We develop a modified Boltzmann equation that captures weak integrability breaking, yielding good agreement between theory and experiment. Our results extend the understanding of integrability and thermalization in low-dimensional quantum systems.