  Universality often emerges in low-energy equilibrium physics of quantum
many-body systems, despite their microscopic complexity and variety. Recently,
there has been a growing interest in studying far-from-equilibrium dynamics of
quantum many-body systems. Such dynamics usually involves highly excited states
beyond the traditional low-energy theory description. Whether universal
behaviors can also emerge in such non-equilibrium dynamics is a central issue
at the frontier of quantum dynamics. Here we report the experimental
observation of universal dynamics by monitoring the spin depolarization process
in a solid-state NMR system described by an ensemble of randomly interacting
spins. The spin depolarization can be related to temporal spin-spin correlation
functions at high temperatures. We discover a remarkable phenomenon that these
correlation functions obey a universal functional form. This experimental fact
helps us identify the dominant interacting processes in the spin depolarization
dynamics that lead to this universality. Our observation demonstrates the
existence of universality even in non-equilibrium dynamics at high
temperatures, thereby complementing the well-established universality in
low-energy physics.
