Self-similar modes of coherent diffusion.

Area of Science:

• Physics
• Quantum Optics
• Nonlinear Dynamics

Background:

• Coherent diffusion describes particle or wave propagation with phase coherence.
• Self-similar solutions represent patterns that maintain their shape while scaling over time.
• Gaussian modes are fundamental solutions in optical diffraction and wave propagation.

Purpose of the Study:

• To derive and experimentally measure self-similar solutions of the coherent diffusion equation.
• To generalize real similarity solutions using nonuniform phases based on Gaussian modes.
• To demonstrate the self-similar evolution of amplitude and phase in diffusing atoms.

Main Methods:

• Derivation of self-similar solutions for the coherent diffusion equation.
• Generalization of solutions using nonuniform phases derived from Gaussian modes.
• Experimental implementation in a light-storage experiment with diffusing atoms.

Main Results:

• Demonstration of self-similar evolution for both amplitude and phase patterns.
• Measurement of an algebraic decay dependent on the mode order.
• Observation of a subset of solutions exhibiting self-similar contraction, contrasting with regular diffusion.

Conclusions:

• Self-similar solutions, including complex ones with nonuniform phases, are experimentally validated for coherent diffusion.
• The study reveals novel dynamics, including self-similar contraction, beyond standard diffusion models.
• Findings have implications for controlling and understanding coherent wave phenomena in diffusing media.