1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates

S. De Nicola, R. Fedele (), D. Jovanovic, B. Malomed, M. A. Man'ko, V. I. Man'ko and P. K. Shukla

The European Physical Journal B: Condensed Matter and Complex Systems, 2006, vol. 54, issue 1, 113-119

Abstract: We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating the external potential well in the three-dimensional (3D) Gross–Pitaevskii equation (GPE). Within the framework of this method, under suitable conditions, the GPE can be exactly decomposed into a pair of coupled equations: a transverse two-dimensional (2D) linear Schrödinger equation and a one-dimensional (1D) longitudinal nonlinear Schrödinger equation (NLSE) with, in a general case, a time-dependent nonlinear coupling coefficient. We review the general idea how to filter and control localized solutions of the GPE. Then, the 1D longitudinal NLSE is numerically solved with suitable non-ideal controlling potentials that differ from the ideal one so as to introduce relatively small errors in the designed spatial profile. It is shown that a BEC with an asymmetric initial position in the confining potential exhibits breather-like oscillations in the longitudinal direction but, nevertheless, the BEC state remains confined within the potential well for a long time. In particular, while the condensate remains essentially stable, preserving its longitudinal soliton-like shape, only a small part is lost into “radiation”. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Keywords: 03.75.Lm Tunneling; Josephson effect; Bose-Einstein condensates in periodic potentials; solitons; vortices; and topological excitations; 05.45.Yv Solitons; 05.30.Jp Boson systems; 03.65.Ge Solutions of wave equations: bound states (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1140/epjb/e2006-00418-0

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