New bright-like soliton solution in quasi-one-dimensional BEC in third order on interaction radius

Details New bright-like soliton solution in quasi-one-dimensional BEC in third order on interaction radius New bright-like soliton solution in quasi-one-dimensional BEC in third order on interaction radius

2011-05-27

arxiv.org/abs/1105.5537v3

Physics

Condensed Matter

Quantum Gases

7 pages, 3 figures

Scientific paper

Nonlinear Schrodinger equations and corresponding quantum hydrodynamic (QHD) equations are widely used in studying ultracold boson-fermion mixtures and superconductors. In this article, we showed that a more exact account for interaction in Bose-Einstein condensate (BEC), compared with the Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of a soliton. We used the first-principle set of equations of QHD in the third order by the interaction radius (TOIR), which corresponds to the GP equation in a first order by the interaction radius. The solution for the soliton in a form of expression for the particle concentration is obtained analytically. The conditions of existence of the soliton are studied; the solution is shown to exist if the interaction between the solitons is repulsive. For the particle concentration of 10^{12}-10^{14} sm^{-3} used experimentally for the BEC, the solution exists if the scattering length is of the order of 1 \mu m, which can be reached using the Feshbach resonance. It is one of the limit case of existence of new solution. The corresponding scattering length decrease with the increasing of concentration of particles. The investigation of effects in the TOIR gives a more detail information on interaction potentials between the atoms and can be used for a more detail investigation into the potential structure.

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