Realization of the driven nonlinear Schrödinger equation with stationary light

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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 Schrödinger 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.