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Russian Physics Journal

On the bright soliton in the Bose–Einstein condensate (to the third order in the interaction radius)

Pavel A. Andreev, Mariya Iv. Trukhanova

Published Apr 1, 2011• 10 citations
Publisher
DOI
10.1007/s11182-011-9548-9

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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.

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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.
Abstract A quantum hydrodynamic model is developed for axial symmetric anisotropic short-range interactions. The quantum stress tensor represents the interaction and is derived up to the third order by the interaction radius. The first order by the interaction radius contains the isotropic part only. This leads to interaction in the Gross–Pitaevskii approximation. Terms existing in the third order by the interaction radius are caused by the isotropic and nonisotropic parts of the interaction, and each of them introduces an interaction constant. Therefore, three interaction constants are involved in the model. Atoms, except for alkali and alkali-earth atoms, can have an anisotropic potential of interaction (this has particularly been demonstrated for the lanthanides). Short-wavelength instability caused by nonlocal terms appears in the Bogoliubov spectrum, and the conditions for stable and unstable behavior are described. Bright solitons in a repulsive Bose–Einstein condensate (BEC) are studied under the influence of anisotropic short-range interaction in the BEC of one species. The area of existence of bright solitons corresponds to the area of instability of the Bogoliubov spectrum. Approximate reduction of nonlocal nonlinearity to quintic nonlinearity in the bright soliton regime is also demonstrated.
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.