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

1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates / S., De Nicola; Fedele, Renato; D., Jovanovic; B., Malomed; M. A., Man'Ko; V. I., Man'Ko; P. K., Shukla. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - STAMPA. - 54:1(2006), pp. 113-119. [10.1140/epjb/e2006-00418-0]

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

FEDELE, RENATO;
2006

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". © EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006.
2006
1D stability analysis of filtering and controlling the solitons in Bose-Einstein condensates / S., De Nicola; Fedele, Renato; D., Jovanovic; B., Malomed; M. A., Man'Ko; V. I., Man'Ko; P. K., Shukla. - In: THE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS. - ISSN 1434-6028. - STAMPA. - 54:1(2006), pp. 113-119. [10.1140/epjb/e2006-00418-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/104238
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