Experimental Results Related to Discrete Nonlinear Schr\"odinger Equations

TL;DR

This paper reviews experimental studies of the discrete nonlinear Schrödinger equations across various physical systems, highlighting recent advances and applications in nonlinear optics, Bose-Einstein condensates, and novel materials.

Contribution

It provides a comprehensive overview of experimental realizations and challenges of DNLS equations in multiple physical contexts, emphasizing recent developments and future directions.

Findings

DNLS equations successfully model pulse propagation in waveguide arrays.

Recent experiments validate DNLS predictions in Bose-Einstein condensates.

DNLS models are increasingly applied to novel materials like metamaterials.

Abstract

In this chapter, we discuss experiments that realize the discrete nonlinear Schr\"odinger (DNLS) equations. The relevance of such descriptions arises from the competition of three common features: nonlinearity, dispersion, and a medium to large level of (periodic, quasiperiodic, or random) discreteness in space. DNLS equations have been especially prevalent in atomic and molecular physics in the study of Bose-Einstein condensates in optical lattices or superlattices; and in nonlinear optics in the description of pulse propagation in waveguide arrays and photorefractive crystals. New experiments in both nonlinear optics and Bose-Einstein condensation provide new challenges for DNLS models, and DNLS and related equations have also recently been used to make important predictions in novel physical settings such as the study of composite metamaterials and arrays of superconducting devices.