Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers

TL;DR

This paper explores the dynamics of optical wave turbulence, revealing both irreversible thermalization and reversible phase-correlated oscillations through theory and fiber experiments.

Contribution

It introduces the coexistence of irreversible thermalization and reversible anomalous correlator dynamics in a conservative optical wave system.

Findings

Irreversible thermalization described by wave turbulence kinetic equations.

Reversible oscillatory dynamics mediated by anomalous correlators.

Experimental confirmation of both regimes in optical fibers.

Abstract

We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear Schr\"odinger equations, describing the polarization evolution of light in a dispersive nonlinear optical fiber. The analysis reveals the emergence of two fundamentally distinct turbulent regimes. In a first regime, the waves undergo a slow, irreversible thermalization process, which is accurately described by the wave turbulence kinetic equation and the associated H-theorem of entropy growth. In stark contrast with this expected irreversible process, we identify a second different regime, where strong phase-correlations spontaneously emerge, giving rise to a fast reversible oscillatory dynamics of the normal correlator and anomalous phase-correlator. Experimental observations confirm the occurrence of both irreversible thermalization and reversible dynamics mediated by the anomalous correlated fluctuations.