  We use femtosecond resonant soft x-ray scattering to measure the ultrafast
optical melting of charge-order correlations in
La$_{1.875}$Ba$_{0.125}$CuO$_4$. By analyzing both the energy-resolved and
energy-integrated order parameter dynamics, we find evidence of a short-lived
nonequilibrium state, whose features are compatible with a sliding charge
density wave coherently set in motion by the pump. This transient state
exhibits shifts in both the quasielastic line energy and its wave vector, as
expected from a classical Doppler effect. The wave vector change is indeed
found to directly follow the pump propagation direction. These results
demonstrate the existence of sliding charge order behavior in an unconventional
charge density wave system and underscore the power of ultrafast optical
excitation as a tool to coherently manipulate electronic condensates.
