TY - JOUR

T1 - Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential

AU - Dos Santos, Mateus C.P.

AU - Malomed, Boris A.

AU - Cardoso, Wesley B.

N1 - Publisher Copyright:
© 2019 IOP Publishing Ltd.

PY - 2019/11/19

Y1 - 2019/11/19

N2 - 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.

AB - 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.

KW - Bose-Einstein condensates

KW - Funnel potential

KW - Gross-Pitaevskii equation

KW - nonpolynomial Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85077768386&partnerID=8YFLogxK

U2 - 10.1088/1361-6455/ab4fb7

DO - 10.1088/1361-6455/ab4fb7

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AN - SCOPUS:85077768386

VL - 52

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 24

M1 - 245301

ER -