3D BEC Bright Solitons under Transverse Confinement: Analytical Results with the Nonpolynomial Schrodinger Equation

Abstract

The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is a nonlinear Schrodinger equation. By imposing a transverse confinement the BEC can travel only in the cylindrical axial direction. We show that in this case the BEC with attractive interaction admits a 3D bright soliton solution which generalizes the text-book one, that is valid in the one-dimensional limit (1D GPE). Contrary to the 1D case, the 3D bright soliton exists only below a critical number of Bosons that depends on the extent of confinement. Finally, we find that the 3D bright soliton collapses if its density excedes a critical value. Our results are obtained by using a nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation derived from the 3D GPE.Comment: 4 pages, presented to the 5th International School/Conference 'Let's Face Chaos through Nonlinear Dynamics', Maribor, July 2002, to be published in Progress in Theoretical Physics Supplemen