双阱势束缚玻色子本征态的Husimi函数及其统计特性  

The Husimi Function of Eigenstates and its Statistical Properties For Bound Bosons in a Double Well Potential

作　　者：赖振讲[1] 赖小伟[2] 薛艳[3] 常峻巍 

机构地区：[1]河南师范大学物理与电子工程学院,新乡453007 [2]河南师范大学新联学院,新乡453007 [3]新乡学院,新乡453007

出　　处：《量子光学学报》2013年第4期301-311,共11页Journal of Quantum Optics

基　　金：河南省教育厅重点实验室培育基金(批准号:2011A140011;13A140544)

摘　　要：借助于两模纠缠相干态,利用Wigner函数的定义和特性,通过严格的数学推导,首先获得了双阱势中玻色子正则规范粒子数差和位相差算符的Wigner函数,然后通过高斯光滑获得了它的Husimi函数。在准线性拉比规范下绘出了8个粒子9个本征态的相空间概率密度分布图;计算了随机变量-数差的均值和方差;从不同角度分析讨论了本征态的统计特性。发现数差的分布不同本征态有不同的结构,分别呈现单峰、双峰、三峰乃至多峰结构,峰的个数随着系统中粒子数的增加而增加;基态和最高激发态呈现单峰结构;且方差较小;分布于基态和最高激发态之间的态具有多峰结构;方差较大,最居中的态方差最大;而相位差的概率密度分布是周期函数,类似于光学里干涉条纹可见度分布,一个周期内总是呈现双峰结构,而且相位差的最可几概率仅有两种选择:0、π和π/2、-π/2.With the aid of the two-mode entangled coherent state,and by precise mathematical derivation, we found a canonical number-phase difference Wigner function for the Bosons in a double well according to the feature and concept of Wigner function.Then through the method of Gaussian smoothing on the Wigner function we obtained its Husimi function.Under the quasilinear Rabi regime,the pictures of the probability density distributions in phase space were plotted with 8bosons 9eigenstates,calculated their expectations and variances of number difference of random variable.The statistical features of the system were discussed under the different way.It was found that there were the structures of the one-peak,two-peak,three-peak and even multi-peak of number-difference distribution,and as the number of particles increased,the number of peaks increased,too.The minimum of variance appeared in the ground state,and the next minimum was in the highest excited state and the most middle state between the ground and highest excited state had the maximum of variance.The phase-difference distribution was a periodic function and similar to the distribution of the interference fringes in the optics.It always presented the two-peak structure in one cycle,and the most probable probability of the phase had only two options：either 0,πor π/2,-π/2.

关 键 词：粒子数差和位相差正则共轭算符对 相空间 Husimi函数 双模哈密顿量 

分 类 号：O431[机械工程—光学工程]