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中文题名:

 新类型广义k-分量非线性荷相干态及其非经典性质    

姓名:

 刘鼎阳    

学科代码:

 070201    

学科专业:

 理论物理    

学生类型:

 硕士    

学位:

 理学硕士    

学位年度:

 2015    

校区:

 北京校区培养    

学院:

 物理学系    

研究方向:

 数学物理    

第一导师姓名:

 刘小明    

第一导师单位:

 北京师范大学物理系    

提交日期:

 2015-06-04    

答辩日期:

 2015-06-03    

外文题名:

 新类型广义k-分量非线性荷相干态及其非经典性质(New type Generalized k-Component nonlinear charge coherent states and their nonclassical properties)    

中文摘要:
新类型广义~k-分量非线性荷相干态定义为荷算符~$Q$~与新类型广义非线性双模算符~$a^kF(N_a)b^kG(N_b)$$(k{\geq}2)~$的~k~个正交归一的共同本征态。此相干态是广义~k-分量非线性荷相干态的推广。本文首先在双模~Fock~空间中,构造了新类型广义~k-分量非线性荷相干态,证明其超完备性。随后借助微分算符的形式实现了~$SU_{fg}(1,1)$~算符在该态的~D~代数表示,得出~$K_-$~算符扮演循环算符的角色。发现了一种能够产生新类型广义~k-分量非线性荷相干态的方法,即由$U(1)$群(荷算符~$Q$~诱导)作用在新类型~k-分量非线性相干态直积连续求和的适当平均来构成,利用纠缠非正交态的观点阐述了新类型广义~k-分量非线性荷相干态是广义纠缠非线性相干态,并且发现分别取~$F(N)=\frac{1}{N},G(N)=\frac{1}{N-1},q=1;F(N)=G(N)=\frac{1}{N},q=0;F(N)=G(N)=\frac{1}{N-1},q=0$~能让新类型广义~k-分量非线性荷相干态分别写成真空压缩态与单光子压缩态的直积,两个真空压缩态的直积以及两个单光子压缩态的直积的连续求和形式。随后研究了新类型广义~k-分量非线性荷相干态的非经典性质,包括~$SU(1,1)$~压缩,单模(双模)压缩以及(N~阶)反聚束性质,主要结果如下:\\(1)证明新类型广义~k-分量非线性荷相干态在~$k\geq3$~时不具备~$SU(1,1)$~压缩性质,但在~$k=2$~时取特殊情况显示~$SU(1,1)$~压缩性质。\\(2)证明新类型广义~k-分量非线性荷相干态不具备单模压缩,双模压缩以及~N~阶单模压缩性质。\\(3)证明新类型广义~k-分量非线性荷相干态在一定条件下会显示反聚束性质或者~N~阶反聚束效应。
外文摘要:
New type generalized~k-Component nonlinear charge coherent states aredefined as the $k~(k{\geq}2)$ orthonormalized eigenstates of the charge operators~$Q$and the new type kth power of the generalized nonlinearannihilation two-mode operators $a^kF(N_a)b^kG(N_b)$. This coherent states are extend from generalized~k-Component nonlinear charge coherent state.The explicit representations of these states are constructed in thetwo-mode Fock space and their (over) completeness proved.A D-algebra realization of the ~$SU_{fg}(1,1)$~ operater corresponding to thesestates has been argued through a differential operator form.These states are shown to be generated by asuitable average over the $U(1)$-group (caused bythe charge operator~$Q$) action on the product of two new type ~k-Component nonlinear coherent states. Thus we can generate these states by thismathematical method.From the entangled nonorthogonal state point of view,they are demonstrated to be generalized entangled nonlinear states.In addition, ~$F(N)=\frac{1}{N},G(N)=\frac{1}{N-1},q=1;F(N)=G(N)=\frac{1}{N},q=0;F(N)=G(N)=\frac{1}{N-1},q=0$~ can make new type generalized~k-Component nonlinear charge coherent states generated by squeezed vacuum state and squeezed single-photon state,two squeezed vacuum states and two squeezed single-photon states respectively.Then nonclassical properties of new type generalized~k-Component nonlinear charge coherent states, such as$SU(1,1)$, one(two)-mode squeezing and (Nth-order) two-mode anti-bunching, are studied. The main results are as follows:\\(1) For $k{\geq3}$, all of the states do not exhibit $SU(1,1)$ squeezing,but for $k=2$,some of these states exhibit $SU(1,1)$ squeezing.\\(2) All of the states do not exhibit do not exhibit one(two)-mode squeezing or Nth-order one-mode squeezing.\\(3) For some nonlinear deformations, new type generalized~k-Component nonlinear charge coherent states exhibit two-mode antibunching or Nth-order antibunching.
参考文献总数:

 53    

馆藏号:

 硕070201/1504    

开放日期:

 2015-06-04    

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