THEORY OF NONLINEAR MATTER WAVES IN OPTICAL LATTICES

TLDR

Matter-wave dynamics in Bose–Einstein condensates within optical lattices exhibit several observable effects. The study investigates modulational instability, solitary, and periodic matter waves, focusing on smooth movable gap solitons and strongly localized discrete modes. The authors derive approximate evolution equations for low‑density condensates, reduce the Gross–Pitaevskii equation to a tight‑binding lattice model, and analyze the effects of Feshbach resonance, linear forces, and lattice defects on nonlinear matter waves.

Abstract

We consider several effects of the matter wave dynamics which can be observed in Bose–Einstein condensates embedded into optical lattices. For low-density condensates, we derive approximate evolution equations, the form of which depends on relation among the main spatial scales of the system. Reduction of the Gross–Pitaevskii equation to a lattice model (the tight-binding approximation) is also presented. Within the framework of the obtained models, we consider modulational instability of the condensate, solitary and periodic matter waves, paying special attention to different limits of the solutions, i.e. to smooth movable gap solitons and to strongly localized discrete modes. We also discuss how the Feshbach resonance, a linear force and lattice defects affect the nonlinear matter waves.