Nonlinear physics in Bose-Einstein condensation

Luis Santos

For sufficiently low temperatures, a Bose gas experiences a transition into a Bose-Einstein condensate, characterized by a macroscopic occupation of the ground state of the system. The development of efficient cooling and trapping techniques for neutral atoms led in 1995, to the first observation of BEC in dilute alkali gases in 87Rb [1]. This remarkable achievement has been followed by BEC experiments in various other elements. The BEC has become during the last years, one of the most active and fruitful research areas of modern atomic physics, constituting an interdisciplinary field, which links atomic physics with various other research areas, like quantum optics, condensed-matter physics, and very especially nonlinear physics.

Lincoln D. Carr

Paulsamy Muruganandam, M. Lakshmanan

This chapter focuses on exploring localized excitations in the variable coefficient nonlinear Schrodinger (NLS) equation and its generalizations. The motivation comes from the fact that the NLS equation and its variants appear in several branches/topics of physics, including nonlinear optics and Bose-Einstein condensates (BECs). The chapter reviews critically the variety of matter wave solitons and their interactions in single- and multi-component Bose-Einstein condensates. It provides a brief overview of the mean Gross- Pitaevskii (GP) equation, derivation of the one-dimensional GP equation, and mapping of the 1D GP equation to the standard NLS equation. The chapter discusses matter wave single and multi bright and dark solitons of Bose– Einstein condensates with varying trap potentials and atomic interactions. It shows various solitons solutions of multi-component BECs described by the two coupled GP equations. In this case, the coupled GP equation has been mapped onto a two coupled NLS equation.

Chuanwei Zhang

Jun Hong, Chenhui Wang, Yongping Zhang

Bose-Einstein condensates (BECs) in periodic potentials generate interesting physics on the instabilities of Bloch states. The lowest-energy Bloch states of BECs in pure nonlinear lattices are dynamically and Landau unstable, which breaks down BEC superfluidity. In this paper we propose to use an out-of-phase linear lattice to stabilize them. The stabilization mechanism is revealed by the averaged interaction. We further incorporate a constant interaction into BECs with mixed nonlinear and linear lattices and reveal its effect on the instabilities of Bloch states in the lowest band.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González