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
  • P. K. Shukla
Statistical and Nonlinear Physics

DOI: 10.1140/epjb/e2006-00418-0

Cite this article as:
De Nicola, S., Fedele, R., Jovanovic, D. et al. Eur. Phys. J. B (2006) 54: 113. doi:10.1140/epjb/e2006-00418-0

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”.

PACS.

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 

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • S. De Nicola
    • 1
  • R. Fedele
    • 2
  • D. Jovanovic
    • 3
  • B. Malomed
    • 4
  • M. A. Man'ko
    • 5
  • V. I. Man'ko
    • 5
  • P. K. Shukla
    • 6
  1. 1.Istituto di Cibernetica “Eduardo Caianiello” del CNR Comprensorio “A. Olivetti” Fabbr. 70, Via Campi Flegrei, 34Pozzuoli (NA)Italy
  2. 2.Dipartimento di Scienze FisicheUniversità Federico II and INFN Sezione di Napoli, Complesso Universitario di M.S. AngeloNapoliItaly
  3. 3.Institute of PhysicsBelgradeSerbia
  4. 4.Department of Interdisciplinary StudiesSchool of Electrical Engineering, Faculty of Engineering, Tel Aviv UniversityTel AvivIsrael
  5. 5.P.N. Lebedev Physical InstituteMoscowRussia
  6. 6.Institut für Theoretische Physik IV and Centre for Plasma Science and Astrophysics, Fakultät für Physik und Astronomie, Ruhr–Universität BochumBochumGermany

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