玻色-爱因斯坦凝聚中的非线性元激发研究

By a detailed analysis for the interatomic interaction in trapping Bose-Einstein condensates (BECs), the property of nonlinear excitations in the BECs is explored in a very general way . A singular perturbation method for inhomogeneous and nonlinear systems is developed and a quasi-one-dimensional (1D) and quasi 2D descriptions of soliton dynamics in BECS are provided. The colliding phase-shifts of 1D dark solitons is shown to be positive. It is found that a lump (a type of localized 2D nonlinear excitation) disintegrates into two vortices when moving into the boundary of BEC . The vortices move in opposite directions along the boundary and merge again into a new lump. A general theoretical method of studying the ground state, linear and nonlinear excitations of low-dimensional BECs is constructed. It is shown that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigen-modes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. A analytical formula for dark soliton radiation and a criterion for dark soliton disintegration are given. An improved saddle-point approximation method is provided which can be used to study the critical temperature of BEC transition, fraction of condensate, fluctuations of condensate, and the effect of finite size and atomic interaction. A new mechanism for decoherence due to condensate fluctuations is proposed. The second harmonic generation of collective modes in a two-component BEC is investigated. It is found that the scattering length of different components can be measured indirectly by using the conversion efficiency of the second harmonic generation. The research on coherent evolution of the BEC in a magnetic trap and an optical lattice potential agrees well with the experimental results by the Pisa group (Italy), leading by Professor E. Arimondo. The research results obtained in this project is significant not only for the basic study of inhomogeneous boson systems but also for revealing new macroscopic quantum phenomenon , like atom laser. There are 14 papers publised in respectively Physical Review (6), Journal of Physics (5) and other international journals (3). The results are cited many times by colleagues home and abroad. The principal investigator of the project has been invited to give two talks in an internatial and a domestic academic conferences.

（1）发展非均匀非线性体系的奇异摄动方法，系统研究碱金属中性原子玻色-爱因斯坦凝聚体中的非线性元激发的产生，传播和相互作用；（2）研究陷阱中元激发的模耦合，谐波产狄萍坝邢尬露刃вΓ唬?）研究多组分凝聚体的非线性干涉。本项目不仅对非均匀玻色气体的基础理论研究，而且对揭示新的宏观量子现象及其应用（如原子激发等）均有重要意义。