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Journal of Hubei Normal University

The evolution of bose-einstein condensate solitons with three-body interaction

Yongshan Cheng, Gong Rong-zhou

Published Jan 1, 2005• 0 citations
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Abstract

The evolution characteristics of the Bose-Einstein Condensate(BEC) soliton with three-body interactions are investigated with a variational approach and direct numerical simulations of the Gross-Pitaevskii-Ginzburg equation.It is found that the effects of the three-body interactions on the evolution characteristics of the BEC soliton are larger than the effecs of the two-body interactions.Its effect depends on the sign of the interactions,the number of atoms in the trap,the coefficient of the trap and the initial pulse width of the BECs soliton.

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The evolution characteristics of the Bose-Einstein Condensate(BEC) soliton with three-body interactions are investigated with a variational approach and direct numerical simulations of the Gross-Pitaevskii-Ginzburg equation.It is found that the effects of the three-body interactions on the evolution characteristics of the BEC soliton are larger than the effecs of the two-body interactions.Its effect depends on the sign of the interactions,the number of atoms in the trap,the coefficient of the trap and the initial pulse width of the BECs soliton.
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The evolution characteristics of the 2-dimension cake-shaped Bose-Einstein Condensate(BEC) soliton trapped in an anisotropy trap are investigated by solving the Gross-Pitaevskii equation with a variational approach.It is found that by introducing an optical lattice potential into certain direction in a columniform symmetrical magnetic trap,a BEC soliton can tend to be stable in that direction and its stability may increase due to the decrease of the soliton expansion in other directions as a result of the coupling effects on those directions.The effects depends on the number of atoms in the trap,the coefficient of the trap and the parameters of the optical lattice potential.
The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.
Beyond the mean-field theory, a new model of the Gross–Pitaevskii equation (GPE) that describes the dynamics of Bose–Einstein condensates (BECs) is derived using an appropriate phase-imprint on the old wavefunction. This modified version of the GPE in addition to the two-body interactions term, also takes into account effects of the three-body interactions. The three-body interactions consist of a quintic term and the delayed nonlinear response of the condensate system term. Then, the modulational instability (MI) of the new GPE confined in an attractive harmonic potential is investigated. The analytical study shows that the three-body interactions destabilize more the condensate system while the external potential alleviates the instability. Numerical results confirm the theoretical predictions. Further numerical investigations of the behavior of solitons reveal that the three-body interactions enhance the appearance of solitons, increase the number of solitons generated and deeply change the lifetime of solitons. Moreover, the external potential delays the appearance of solitons. Besides, a new initial condition is introduced which enables to increase the number of solitons created and deeply affects the trail of chains of solitons generated. Moreover, the MI of a condensate without the external potential, and in a repulsive potential is also investigated.