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Charge order is universal among high-T$_c$ cuprates but its relevance tosuperconductivity is not established. It is widely believed that, while staticorder competes with superconductivity, dynamic order may be favorable and evencontribute to Cooper pairing. We use time-resolved resonant soft x-rayscattering to study the collective dynamics of the charge order in theprototypical cuprate, La$_{2-x}$Ba$_x$CuO$_4$. We find that, at energy scales$0.4$ meV $ \lesssim \omega \lesssim 2$ meV, the excitations are overdamped andpropagate via Brownian-like diffusion. At energy scales below 0.4 meV thecharge order exhibits dynamic critical scaling, displaying universal behaviorarising from propagation of topological defects. Our study implies that chargeorder is dynamic, so may participate tangibly in superconductivity.

Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La$_{2-x}$Ba$_x$CuO$_4$