Bright solitons in ultracold atoms
arXiv:1710.05335 · doi:10.1007/s11082-017-1247-5
Abstract
We review old and recent experimental and theoretical results on bright solitons in Bose-Einstein condensates made of alkali-metal atoms and under external optical confinement. First we deduce the three-dimensional Gross-Pitaevskii equation (3D GPE) from the Dirac-Frenkel action of interacting identical bosons within a time-dependent Hartree approximation. Then we discuss the dimensional reduction of the GPE from 3D to 1D, deriving the 1D GPE and also the 1D nonpolynomial Schrödinger equation (1D NPSE). Finally, we analyze the bright solition solutions of both 1D GPE and 1D NPSE and compare these theoretical predictions with the available experimental data.
arXiv comment12 pages, 4 figures, tutorial talk at the VI International School and Conference on Photonics "Photonica 2017", 28 August - 1 September 2017, Belgrade, Serbia; new version: added one figure and some references, corrected typos
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- Stable high-dimensional weak-light soliton molecules and their active control
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- Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions
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