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

## TL;DR

This study measures the phase-space density of ultra-cold atoms undergoing anomalous diffusion, revealing a power-law decay in position-velocity correlation that is explained by a scaling theory and confirmed through simulations.

## Contribution

It introduces a direct tomographic method to measure PSDD and demonstrates a universal power-law decay in correlation functions in anomalous diffusion.

## Key findings

- Power-law decay of position-velocity correlation function observed.
- Scaling theory successfully explains the decay behavior.
- Monte-Carlo simulations confirm the universality of the scaling law.

## 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.