Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential

Mateus C.P. Dos Santos, Boris A. Malomed, Wesley B. Cardoso

Research output: Contribution to journalArticlepeer-review


Starting from the standard three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D-NPSE) governing the axial dynamics of atomic Bose-Einstein condensates (BECs) under the action of a singular but physically relevant funnel-shaped transverse trap, i.e. an attractive 2D potential ∼-1/r (where r is the radial coordinate in the transverse plane), in combination with the repulsive self-interaction. Wave functions of the trapped BEC are regular, in spite of the potential's singularity. The model applies to a condensate of particles (small molecules) carrying a permanent electric dipole moment in the field of a uniformly charged axial thread, as well as to a quantum gas of magnetic atoms pulled by an axial electric current. By means of numerical simulations, we verify that the effective 1D-NPSE provides accurate static and dynamical results, in comparison to the full 3D GPE, for both repulsive and attractive signs of the intrinsic nonlinearity.

Original languageEnglish
Article number245301
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Issue number24
StatePublished - 19 Nov 2019


  • Bose-Einstein condensates
  • Funnel potential
  • Gross-Pitaevskii equation
  • nonpolynomial Schrödinger equation


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