Nonlinear Phenomena and their Controls in Bose-Einstein Condensates

玻色-爱因斯坦凝聚中的非线性现象及其控制

基本信息

批准号：
14540373
负责人：
WADATI Miki
金额：
$ 1.92万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

To clarify the static and dynamic properties of the Bose-Einstein condensates of ultra-cold neutral bosonic atoms, the following subjects were investigated.1. Quantum delta-function gasesFor one-dimensional quantum integrable particle systems, quasi-momentum distribution and excitation energy spectrum are described by Lieb-Liniger (LL) integral equation and Yang-Yang (YY) integral equation, respectively. Those integral equations are usually solved numerically, but the analytic work are few. In particular, the weak coupling case is known to be a hard problem. We apply the power-series expansion method for analysis of spin-1/2 fermion system where two kinds of fermions (spin up and spin down) interact through the attractive delta-function potential. In the strong coupling region, spin-pair states are shown to exist. This implies the occurrence of BCS state in ultra-cold gases.2. Matter-wave propagations in F=1 spinor BEC condensate.In optical trap, the condensates with internal degrees of freedom are realized. It was found that, when the magnitudes of inter-atomic potential and spin-exchange interaction are same, three-component Gross-Pitaevskii (GP) equation is integrable. Through the inverse scattering method, N-soliton solutions are obtained. For the attractive case, bright solitons exist and those are classified into polar soliton and ferromagnetic soliton. For the repulsive case, the similar results hold (in preparation). For general two coupling constants, matter-wave propagations are investigated. From the analysis of plane-wave solutions, we can show the existence of polar soliton and ferromagnetic soliton.Since this year is the final year of the project, we extended analyses to the subjects such as soliton equations in non-commutative space-time, transports in one-dimensional exclusion processes and, geometric phases and quantum entanglements of two spins in a magnetic field.

为了阐明超冷中性骨气原子的Bose-Einstein冷凝物的静态和动态特性，研究了以下受试者1。 Lieb-Liniger（LL）积分方程和Yang-Yang（YY）积分方程分别描述了用于一维量子整合粒子系统，准摩膜分布和激发能谱的量子三角功能气体。这些积分方程通常是数值求解的，但是分析工作很少。特别是，较弱的耦合案例已知是一个严重的问题。我们将功率系列扩展方法应用于Spin-1/2 Fermion系统的分析，其中两种费米子（向上旋转和旋转）通过有吸引力的Delta功能潜力相互作用。在强耦合区域中，旋转对状态被证明存在。这意味着BCS状态在超冷气中的发生。2。 f = 1纺丝bec冷凝物中的物质波传播。在光学陷阱中，具有内部自由度的冷凝物。已经发现，当原子间电位和自旋交换相互作用的幅度相同时，三个成分的gross-pitaevskii（GP）方程是可集成的。通过反向散射方法，获得N-索氏溶液。对于有吸引力的情况，存在明亮的孤子，这些孤子被分类为极性孤子和铁磁孤子。对于排斥案例，相似的结果（准备）。对于一般两个耦合常数，研究物质波传播。从对平面波解决方案的分析中，我们可以显示出极性孤子和铁磁孤子的存在。今年是该项目的最后一年，我们将分析扩展到了诸如非交互式时空的孤子方程，在磁场中两个旋转的几维排除过程以及几何阶段和量子纠缠中的传输。