Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system

Abstract

The integrable nonlinear Schrödinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integrability over sufficiently long distances to observe recurrence, as well as synthesizing and measuring the field in both amplitude and phase on the picosecond timescales of typical experiments is challenging. Here we report on the experimental realization of FPUT recurrence in terms of an exact space-time-periodic solution of the integrable NLSE in a testbed for optical communication experiments. The complex-valued initial condition is constructed by means of the finite-gap integration method, modulated onto the optical carrier driven by an arbitrary waveform generator and launched into a recirculating fiber loop with periodic amplification. The measurement with an intradyne coherent receiver after a predetermined number of revolutions provides a non-invasive full-field characterization of the space-time dynamics. The recurrent space-time evolution is in close agreement with theoretical predictions over a distance of 9000 km. Nonlinear spectral analysis reveals an invariant nonlinear spectrum. The space-time scale exceeds that of previous experiments on FPUT recurrence in fiber by three orders of magnitude.

arXiv commentVersion accepted for publication in Scientific Reports

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Cited by in corpus (10)

• Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
• Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation
• Space-time observation of the dynamics of soliton collisions in a recirculating optical fiber loop
• Observation of the noise-driven thermalization of the Fermi-Pasta-Ulam-Tsingou recurrence in optical fibers
• Spatio-temporal observation of higher-order modulation instability in a recirculating fiber loop
• Trajectory control in idealized four-wave mixing processes in optical fiber
• Data Transmission based on Exact Inverse Periodic Nonlinear Fourier Transform, Part II: Waveform Design and Experiment
• Controlled manipulation of solitons in a recirculating fiber loop using external potentials
• Nonlinearity accelerates the thermalization of the quartic FPUT model with stochastic baths
• Chaotic behaviour of disordered nonlinear lattices