Atomic and Molecular Physics,\
    Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences,\
    Wuhan, 430071, P. R. China 
- 'Department of Physics, Hunan Normal University, Changsha, 410081, P. R. China'
- 'Department of Physics, University of Waterloo, Waterloo, Ontario, N2L3G1,Canada'
author:
- 'Chaohong Lee, Lei Shi, Xiwen Zhu, Kelin Gao'
- 'Wenhua Hai, Yiwu Duan'
- 'Wing-Ki Liu'
title: 'Chaotic atomic population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric trap potential '
---

Introduction
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The study of Bose-Einstein condensate (BEC) in gases can give new understanding of atomic, condensed-matter, and statistical physics. Due to the remarkable development in the ability to control atomic motion by optical techniques, BEC was first produced in a weakly interacting gas of alkali metal atoms held in magnetic trap in 1995 \[1\]. Following the first observation, many important experiments were carried out. The group of Durfee and Ketterle detected the condensate in cooled gases, the collective excitations, the collisions between separately-prepared condensates, and the pulsed output of a prototype atom laser \[2,3\], they also observed the interference between two Bose condensates and demonstrated that Bose condensed atoms are $``$laser-like$"$, that is, they are coherent and show long-range correlations \[4\]. These 