Prethermalization in a quenched one-dimensional quantum fluid of light: Intrinsic limits to the coherent propagation of a light beam in a nonlinear optical fiber

TL;DR

This paper investigates how a laser beam's coherence degrades after passing through a nonlinear optical fiber, revealing prethermalization phenomena and light-cone propagation of correlations in a quantum photon fluid.

Contribution

It introduces a quantum quench model for photon interactions in a nonlinear fiber and predicts prethermalization and light-cone correlation spreading using Bogoliubov theory.

Findings

Correlations form a prethermalized state locally.

Correlations propagate at the Bogoliubov speed of sound.

Long-term coherence of the light beam diminishes.

Abstract

We study the coherence properties of a laser beam after propagation along a one-dimensional lossless nonlinear optical waveguide. Within the paraxial, slowly-varying-envelope, and single-transverse-mode approximations, the quantum propagation of the light field in the nonlinear medium is mapped onto a quantum Gross-Pitaevskii-type evolution of a closed one-dimensional system of many interacting photons. Upon crossing the entrance and the back faces of the waveguide, the photon-photon interaction parameter undergoes two sudden jumps, resulting in a pair of quantum quenches of the system's Hamiltonian. In the weak-interaction regime, we use the modulus-phase Bogoliubov theory of dilute Bose gases to describe the quantum fluctuations of the fluid of light and predict that correlations typical of a prethermalized state emerge locally in their final form and propagate in a light-cone way at the Bogoliubov speed of sound in the photon fluid. This peculiar relaxation dynamics, visible in the light exiting the waveguide, results in a loss of long-lived coherence in the beam of light.