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.
Highlights
Following a long series of developments in the experimental techniques of atomic and optical physics, the Bose–Einstein condensation (BEC) of cold alkali atomic gases was realized in 1995(see, e.g., [1,2,3] and references therein)
Owing to the general nature of swallowtail shaped dispersions resulting from the interplay of atom-atom interactions and periodicity, they have been predicted to occur in a variety of systems different from the setting mainly considered in this review—namely that of BECs in an optical lattice with effectively 1D dynamics
This situation is similar to superfluid Fermi gases in a periodic potential, where the swallowtail appears due to the effect of the nonlinear interaction dominating over the periodicity of the system induced by the external potential [69]
Summary
Following a long series of developments in the experimental techniques of atomic and optical physics, the Bose–Einstein condensation (BEC) of cold alkali atomic gases was realized in 1995. The creation of this new state of quantum matter has opened up a new research field, the physics of ultracold atomic gases The novelty of this system lies in its high controllability: various system parameters such as the dimensionality, the configuration of the external potentials, and the strength and the sign of the inter-atomic interaction can be manipulated dynamically as well as statically. Equipped with Feshbach resonance, a knob for controlling the strength of the nonlinearity, cold atomic gases in optical lattices allow us to enter a regime in which the effect of the nonlinearity is comparable to (or even dominates over) that of the periodic potential Such a strongly nonlinear regime beyond the tight-binding approximation has not been well-explored in conventional solid state physics.
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