A universal speed limit for spreading of coherence

Discoveries of fundamental limits for the rates of physical processes, from the speed of light to the Lieb-Robinson bound for information propagation, often lead to breakthroughs in the our understanding of the underlying physics. Here we observe such a limit for a paradigmatic many-body phenomenon, the spreading of coherence during formation of a weakly interacting Bose-Einstein condensate. We study condensate formation in an isolated homogeneous atomic gas that is initially far from equilibrium, in an incoherent low-energy state, and condenses as it relaxes towards equilibrium. Tuning the inter-atomic interactions that drive condensation, we show that the spreading of coherence through the system is initially slower for weaker interactions, and faster for stronger ones, but always eventually reaches the same limit, where the square of the coherence length grows at a universal rate given by the ratio of Planck's constant and the particle mass, or equivalently by the quantum of velocity circulation associated with a quantum vortex. These observations are robust to changes in the initial state, the gas density, and the system size. Our results provide benchmarks for theories of universality far from equilibrium, are relevant for quantum technologies that rely on large-scale coherence, and invite similar measurements in other systems.