Title: Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion,
Abstract: In this letter we present a measurement of the phase-space density
distribution (PSDD) of ultra-cold \Rb atoms performing 1D anomalous diffusion.
The PSDD is imaged using a direct tomographic method based on Raman velocity
selection. It reveals that the position-velocity correlation function
$C_{xv}(t)$ builds up on a timescale related to the initial conditions of the
ensemble and then decays asymptotically as a power-law. We show that the decay
follows a simple scaling theory involving the power-law asymptotic dynamics of
position and velocity. The generality of this scaling theory is confirmed using
Monte-Carlo simulations of two distinct models of anomalous diffusion.