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

Area of Science:

• Atomic physics
• Quantum mechanics
• Statistical mechanics

Background:

• Anomalous diffusion deviates from standard Brownian motion.
• Understanding particle dynamics in complex systems is crucial.
• Phase-space density distribution (PSDD) provides a complete description of particle ensembles.

Purpose of the Study:

• To measure the PSDD of ultracold Rubidium-87 atoms in 1D anomalous diffusion.
• To investigate the time evolution of the position-velocity correlation function.
• To validate a scaling theory for anomalous diffusion dynamics.

Main Methods:

• Direct tomographic imaging of the PSDD using Raman velocity selection.
• Measurement of the position-velocity correlation function C_{xv}(t).
• Monte Carlo simulations of anomalous diffusion models.

Main Results:

• The PSDD of ultracold atoms was successfully measured.
• The position-velocity correlation function exhibits buildup and subsequent power-law decay.
• The observed decay dynamics align with a proposed scaling theory.

Conclusions:

• The study provides experimental evidence for anomalous diffusion in ultracold atoms.
• A scaling theory effectively describes the asymptotic dynamics of position and velocity.
• The findings are generalizable and confirmed by simulations.