Long-lived periodic revivals of coherence in an interacting Bose-Einstein condensate

We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field-driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to $0.75$ at the evolution time of $1.5$ s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of $2.8$ s for a trapped condensate of $5.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ interacting atoms.