Realization of the driven nonlinear Schr\"odinger equation with stationary light

TL;DR

This paper presents a flexible slow light platform using cold atoms to realize the driven nonlinear Schrödinger equation with a potential, enabling advanced studies of nonlinear out-of-equilibrium physics.

Contribution

It introduces a novel slow light setup that allows dynamic control of nonlinearities and potentials for studying driven nonlinear Schrödinger dynamics.

Findings

Demonstrates the platform's ability to simulate driven nonlinear Schrödinger equations.

Shows tunability of nonlinearities and potentials in the setup.

Provides a new tool for exploring nonlinear out-of-equilibrium phenomena.

Abstract

We introduce a versatile platform for studying nonlinear out-of-equilibrium physics. The platform is based on a slow light setup where an optical waveguide is interfaced with cold atoms to realize the driven nonlinear Schr\"odinger equation with a potential. We compare the proposed setup with similar setups using Bose-Einstein condensates and investigate the system's response under coherent driving for a lattice potential. The slow light setup provides novel angles in the study of nonlinear dynamics due to its advantages in introducing and modulating the driving, the extra tunability over the sign and strength of the available nonlinearities, and the possibility to electromagnetically carve out the underlying potential on demand.