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

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.

19 pages, 3 figures

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• Interferences between Bogoliubov excitations and their impact on the evidence of superfluidity in a paraxial fluid of light
• Momentum distribution and coherence of a weakly interacting Bose gas after a quench
• Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide
• Postquench prethermalization in a disordered quantum fluid of light
• Classical Casimir force from a quasi-condensate of light
• Quantum Squeezing of Slow-Light Dark Solitons via Electromagnetically Induced Transparency
• Quantum Squeezing of Slow-Light Solitons
• Spatio-temporal equilibrium thermodynamics of guided optical waves at positive and negative temperatures
• Critical speed of a binary superfluid of light