【作者】 刘志荣；

【导师】 刘正东；

【作者基本信息】 南昌大学 ， 理论物理， 2006， 硕士

【摘要】 当粒子的总自旋为h的整数倍时被称为玻色子，如光子、玻色原子和玻色分子等，它们服从玻色—爱因斯坦量子统计。当绝对温度下降到0 k附近，理想的量子玻色气体将发生相变，这时玻色子的德布罗意波长大于粒子间的平均距离(即λ_dB＞d)。这一现象早在1924年就被玻色和爱因斯坦预言，因而称之为玻色-爱因斯坦凝聚（Bose-Einstein condensation，简称BEC）。BEC最基本的特征是：当玻色气体的温度低于某一相变跃迁温度时，大量的玻色子将聚集在能量最低的宏观量子相干态（基态），如同激光中的大量玻色光子群聚在宏观的光子相干态一样。自从玻色和爱因斯坦预言BEC以来，人们就BEC的实现及其量子统计性质进行了长期深入系统的理论研究与实验探索，并取得了一系列重大的实验进展。迄今为止，国际上已有40余个实验室采用各种冷却、囚禁与操控技术实现了八种元素的原子BEC，即具有正散射长度碱金属原子(²³Na，⁸⁷Rb)的BEC；具有负散射长度碱金属原子(⁷Li，⁴¹K，⁸⁵Rb，¹³³Cs)的BEC；自旋极化¹H原子、亚稳态⁴He原子和具有2个价电子的¹⁷⁴Yb稀土原子的BEC以及由费米原子形成的⁶Li₂和⁴⁰K₂分子BEC。此外，实现BEC的实验方案可分为磁囚禁BEC，全光型BEC，双阱BEC，微阱BEC，双样品BEC和低维BEC等。 本论文就二分量BEC动力学行为进行了理论研究： 运用数值模拟方法研究了当二分量BEC初始具有相同的原子数时，二分量BEC原子数密度的短时动力学行为，讨论了驱动场耦合强度、不同分量间原子作用强度、射频场频率及同分量内原子间作用强度对二分量原子数密度演化特性的影响。结果显示：在较短的时间内，原子数密度随时间近似作周期性振荡，其振荡的周期随驱动耦合场强度、不同分量原子间作用强度的增大而减小，振荡的周期随随自耦合强度的增大而增大；射频场频率的变化并不显著改变原子数密度振荡的周期，但它的增大会和自耦合强度的增大一样导致原子密度振荡的振幅减小。 运用数值模拟研究了二分量BEC原子数密度的长时动力学行为，讨论了驱动场Rabi频率、二分量初始相对相位差、驱动场耦合强度、同分量内原子作用强度及不同分量间原子作用强度对二分量BEC第二分量原子数密度演化特性的更多还原

【Abstract】 In this thesis , we study the following problems about two-component Bose-Einstein condensates (BEC) in theory:In chapter 2 , with the numerical calculation method we have investigated the dynamics of two-component BEC with coupling drive by the explicit expression of the second atomicity density , and we have also discussed the influence of the strength of the coupling drive .The strength of interspecies interaction , the rf frequencies and the strength of the interaction in each condensate on the time evolution properties of atomicity density is studied . Our results demonstrate that atomicity density fluctuates like a sinusoidal function of time approximately . And it is clear that with the increase of the strength of coupling drive or the strength of interspecies interaction , the period of oscillation of the atomicity density decreases . However , its period increases with the increase of the strength of the interaction in each condensate . Furthermore , the change of the rf frequencies does not affect fluctuation’s period notably , both the increase of the rf frequencies and the strength of the interaction in each condensate will result in the decrease of the amplitude of oscillation.In chapter 3 , we have investigated the time evolution of atomicity density of two-component BEC with numerical calculation , and have found that the evolution of condensate density in long time , which presents a typical quantum collapse and revival with a complex period , is rather different from that in short time ,which displays a regular sinusoidal oscillation. Furthermore ,we have also discussed the influence of the Rabi frequency of coupling drive field .various values for the relative phase ,the strength of the coupling drive , the strength of the interatomic interaction in each condensate and the strength of the interspecies interaction on the evolution properties of atomicity density .In chapter 4 the influence of rf (radio frequency) frequencies on long time evolution of atomicity density of two-component Bose-Einstein condensations is studied . The research results demonstrate that the atomicity density of BEC更多还原