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Chinese Optics Letters

Effects of external magnetic trap on two dark solitons of a two-component Bose-Einstein condensate

李宏 Hong Li, D. N Wang

Published Jan 1, 2008• 5 citations
Publisher

Abstract

Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap, and effects of the trap potential on their dynamics are investigated by the numerical simulation.The results show that the dark solitons attract, collide and repel periodically in two components as time changes, the time period depends strictly on the initial condition and the potential, and there are obvious self-trapping effects on the two dark solitons.

DOI
10.3788/col20080608.0611

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Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap, and effects of the trap potential on their dynamics are investigated by the numerical simulation.The results show that the dark solitons attract, collide and repel periodically in two components as time changes, the time period depends strictly on the initial condition and the potential, and there are obvious self-trapping effects on the two dark solitons.
The dynamics of dark soliton in a growing Bose–Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.
The dynamics of a dark soliton has been investigated in a Bose–Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.
Two coupled dark solitons are considered in a two-component Bose–Einstein condensate, and their dynamics are investigated by the variational approach based the renormalized integrals of motion. The stationary states as physical solutions to the describing equations are obtained, and the dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field. The switching and self-trapping dynamics of the coupled dark vector solitons are discussed by the evolution of the atom population transferring ratio.
We investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.
The motion of a dark soliton in one-dimensional Bose-Einstein condensates with an expulsive parabolic potential is investigated.Furthermore,the dynamics of dark soliton and the interaction between two dark solitons are discussed in detail by numerical simulation.The results show that the motion of dark soliton is periodical,and the interaction between two dark solitons exhibits to collide each other periodically.As the separation between two dark solitons becomes shorter,the periodical colliding is shrinking and the period of the colliding action is shorter.It is meaning for us to understand the dynamics of microphysical field.
This paper investigates the dynamics of dark solitons in a Bose–Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.