Observation of the evolution from a microcanonical ensemble to a canonical ensemble in a quasi-one-dimensional Bose gas

We report the observation of a continuous evolution from a microcanonical ensemble to a canonical ensemble in a quasi-one-dimensional Bose gas by preparing a prethermal state and tracking its longtime evolution. The prethermal state is prepared by a rapid dephasing process that preserves axial energy and establishes a microcanonical-like plateau distribution. Next comes a slow (seconds-long) relaxation driven by weak integrability breaking. By extracting the parameters of the Wigner-space distribution, we find the thermalization rate is controlled by the atomic interaction. Using a model of one-dimensional inelastic collisions that excite transverse modes and violate axial energy conservation, we quantify the approach to the canonical ensemble from a prethermal state. Our results establish a quantitative and experimentally validated pathway from prethermal state in the near-integrable regime to full thermal equilibrium in a weakly nonintegrable quantum gas. It is noteworthy that we use a deep-learning-assisted DAE(denoising autoencoder) to improve our data-processing.