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arXiv:1205.1161 · The European Physical Journal D

Soliton appearing in boson-fermion mixture at the third order of the interaction radius

Konstantin V. Zezyulin, Pavel A. Andreev, L. S. Kuz’menkov

Published Jul 1, 2013• 6 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2013-30418-x

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Abstract Repulsive Bose–Einstein condensates, where short-range interaction is included up to the third order by the interaction radius, demonstrate the existence of bright solitons in a narrow interval of parameters. These solitons are studied here for the boson–fermion mixture, where spin-1/2 fermions are considered in the regime of full-spin polarization. The influence of fermions on bosonic bright solitons via the boson–fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered within the hydrodynamic model, which includes the kinetic pressure-evolution equation. The interactions between fermions are also considered. The first order by the interaction radius makes a zero contribution to the Euler equation and the kinetic pressure evolution equation for fermions, but the third order by the interaction radius provides nonzero contributions to both equations. The repulsive (attractive) boson–fermion interaction leads to bright (dark) fermionic solitons.
Nonlinear Schrödinger equations and corresponding quantum hydrodynamic (QHD) equations are widely used in studying of ultracold boson–fermion mixtures and superconductors. In this article, we show that more exact account of interaction in Bose–Einstein condensate (BEC), in comparison with the Gross–Pitaevskii (GP) approximation, leads to the existence of a new type of solitons. We use a set of QHD equations in the third order by the interaction radius (TOIR), which corresponds to the GP equation in the first order by the interaction radius. We analytically obtain a soliton solution which is an area of increased atom concentration. The conditions for existence of the soliton are studied. It is shown what solution exists if the interaction between the particles is repulsive. Particle concentration has been achieved experimentally for the BEC is of order of 1012–1014 cm-3. In this case the solution exists if the scattering length is of the order of 1 μm, which can be reached using the Feshbach resonance. It is one of the limit case of existence of the solution. The corresponding scattering length decrease with the increasing of concentration of particles. We have shown that account of interaction up to TOIR approximation leads to new effects. The investigation of effects in the TOIR approximation gives a more detail information on interaction potentials between the atoms and can be used for a more detail investigation of the interatomic potential structure.