Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential

doi:10.1088/1674-1056/20/4/040310

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40310-040310.doi: 10.1088/1674-1056/20/4/040310

Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential

方见树, 廖湘萍

Institute of Physics, Hunan University of Technology, Zhuzhou 412008, China

收稿日期:2010-10-22 修回日期:2010-11-15 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 10JJ3088) and the Key Research Foundation of the Education Bureau of Hunan Province of China (Grant Nos. 08A015 and 10A026).

Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential

Fang Jian-Shu(方见树)^a)b)† and Liao Xiang-Ping(廖湘萍)^a)

^aInstitute of Physics, Hunan University of Technology, Zhuzhou 412008, China; ^b College of Science, Hunan University of Technology, Zhuzhou 412008, China

Received:2010-10-22 Revised:2010-11-15 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 10JJ3088) and the Key Research Foundation of the Education Bureau of Hunan Province of China (Grant Nos. 08A015 and 10A026).

摘要/Abstract

摘要： Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

关键词: Bose--Einstein condensate, chaos, stability, tilted optical lattice potential

Abstract: Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.

Key words: Bose--Einstein condensate, chaos, stability, tilted optical lattice potential

中图分类号: (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

03.75.Lm

05.45.Ac (Low-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)

方见树, 廖湘萍. Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential[J]. 中国物理B, 2011, 20(4): 40310-040310.

Fang Jian-Shu(方见树) and Liao Xiang-Ping(廖湘萍) . Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential[J]. Chin. Phys. B, 2011, 20(4): 40310-040310.

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Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential

Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential

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