Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States

TL;DR

This paper reviews nonlinear phenomena in ultracold atomic gases within optical lattices, highlighting novel features like energy band loops, multiple periodicity states, and nonlinear lattice effects arising from the interplay of nonlinearity and periodicity.

Contribution

It provides a comprehensive overview of recent advances in understanding nonlinear effects in extended states of ultracold gases in optical lattices, emphasizing new phenomena and their underlying mechanisms.

Findings

Identification of swallowtail loop structures in energy bands

Observation of Bloch states with multiple periodicities

Analysis of nonlinear lattice systems with spatially periodic interactions

Abstract

The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes "swallowtail" loop structures of the energy band, Bloch states with multiple periodicity, and those in "nonlinear lattices", i.e., systems with the nonlinear interaction term itself being a periodic function in space.