We perform Ramsey spectroscopy on the ground state of ultracold 87 Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should reduce the contrast of the Ramsey frindges by a factor of 5 for 5 s of interrogation. We measure hardly any decay, only a factor 1.08 corresponding to a coherence time of the order of one minute. This new effect allows us to increase the quality factor of the microwave atomic resonance. We explain this surprising result by

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... a spin self-rephasing mechanism induced by the identical spin rotation effect. The study of decoherence under metrological condition is the key to this synchronisation regime where non-linear effects dominate the evolution of the cloud. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and may appear in other physical systems with trapped atoms. In particular, this effect will exist for fermions and could be exploited to enhance the stability of optical lattice clocks.