Quasi-one-dimensional approximation for Bose–Einstein condensates transversely trapped by a funnel potential
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2019
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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.
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SANTOS, Mateus C. P. dos; MALOMED, Boris A.; CARDOSO, Wesley B. Quasi-one-dimensional approximation for Bose-Einstein condensates transversely trapped by a funnel potential. Journal of Physics B: atomic molecular and optical physics, Bristol, v. 52, e245301, 2019. DOI: 10.1088/1361-6455/ab4fb7. Disponível em: https://iopscience.iop.org/article/10.1088/1361-6455/ab4fb7. Acesso em: 1 jun.2023.