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In this letter we present a measurement of the phase-space densitydistribution (PSDD) of ultra-cold \Rb atoms performing 1D anomalous diffusion.The PSDD is imaged using a direct tomographic method based on Raman velocityselection. It reveals that the position-velocity correlation function$C_{xv}(t)$ builds up on a timescale related to the initial conditions of theensemble and then decays asymptotically as a power-law. We show that the decayfollows a simple scaling theory involving the power-law asymptotic dynamics ofposition and velocity. The generality of this scaling theory is confirmed usingMonte-Carlo simulations of two distinct models of anomalous diffusion.

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion