Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement

Details Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement Generalized nonpolynomial Schrodinger equations for matter waves under anisotropic transverse confinement

2009-07-07

arxiv.org/abs/0907.1248v1

J. Phys. A: Math. Theor. 42 (2009) 335205

Physics

Condensed Matter

Quantum Gases

9 pages, 2 figures, to be published in Journal of Physics A: Math. Theor

Scientific paper

Starting from the three-dimensional Gross-Pitaevskii equation we derive a 1D generalized nonpolynomial Schrodinger equation, which describes the dynamics of Bose-Einstein condensates under the action of a generic potential in the longitudinal axial direction and of an anisotropic harmonic potential in the transverse radial direction. This equation reduces to the familiar 1D nonpolynomial Schrodinger equation [Phys. Rev. A 65, 043614 (2002)] in the case of isotropic transverse harmonic confinement. In addition, we show that if the longitudinal potential models a periodic optical lattice the 3D GPE can be mapped into a 1D generalized discrete nonpolynomial Schrodinger equation.

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