奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance

For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number- phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coettlcient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.     

New approach for deriving the exact time evolution of density operator for diffusive anharmonic oscillator and its Wigner distribution function

Using the thermal entangled state representation, we solve the master equation of a diffusive anharmonic oscillator (AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation. We present a new evolution formula of the Wigner function (WF) for any initial state of the diffusive AHO by converting the calculation of the WF to an overlap between two pure states in an enlarged Fock space. It is found that this formula brings us much convenience to investigate the WF's evolution of any known initial state. As applications, this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of the diffusive AHO.     

新的奇偶非线性相干态及其非经典性质

构造出了一种新的奇偶非线性相干态, 并借助于数值计算方法研究了它们的压缩、振幅平方压缩、反聚束和相位概率分布等非经典性质. 结果表明, 与通常的奇偶相干态和非线性奇偶相干态不同, 在参数|λ|的不同取值范围内, 新的奇偶非线性相干态在Y₁和Y₂两个方向均可呈现振幅平方压缩效应, 而压缩效应仅在偶非线性相干态的X₂方向上呈现, 反聚束效应仅在奇非线性相干态中呈现. 另外, 通过研究新的奇偶非线性相干态相位概率分布, 发现新的奇偶非线性相干态具有完全不同的量子干涉特性. 关键词： 新的奇偶非线性相干态 压缩效应 反聚束 相位概率分布     

量子比特的普适远程翻转和克隆

提出一种把量子隐形传态、最佳普适量子比特翻转和最佳普适量子克隆三者结合起来的量子比特普适远程翻转和克隆方案.当发送者和处于不同地点的三个接收者共享一个特定的四粒子纠缠态作为量子信道时,通过发送者的Bell基测量、经典通信和各个接收者的局域幺正变换,一个接收者能够以2/3的最佳保真度得到一份原未知量子比特的正交补态,另外两个接收者能够分别以5/6的最佳保真度得到原未知量子比特的一份拷贝.此方案用较少的量子纠缠资源同时完成了未知量子比特的普适远程翻转和克隆,且其保真度分别达到了最佳.实现此方案的关键在于构造出发送者和接收者共享的特定四粒子纠缠态作为量子信道,分析了此特殊四粒子态内在的纠缠结构.     

Wigner function for the generalized excited pair coherent state

This paper introduces the generalized excited pair coherent state （GEPCS）. Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state ｜η1, η2, τ1, τ2｜. The entangled states ｜η〉 and ｜η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.     

Quasiprobability distributions of a new kind of even and odd nonlinear coherent states

Using a numerical computational method, quasiprobability distributions of new kinds of even and odd nonlinear coherent states (EONLCS) are investigated. The results show that the distributions of the new even nonlinear coherent states (NLCS) are distinct from those of the new odd NLCS and imply that the new EONLCS always exhibit some different nonclassical effects. Finally, with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics, the tomograms of the new EONLCS are calculated. This is a new way of obtaining the tomogram function.     

New approach for deriving the exact time evolution of the density operator for a diffusive anharmonic oscillator and its Wigner distribution function

Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator(AHO) to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function(WF) for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF’s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.     

Normal coordinate in harmonic crystal obtained virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.     

有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

构造出了有限维Hilbert空间Roy型奇偶非线性相干态, 讨论了它们的正交归一完备性和振幅平方压缩效应. 研究表明, 在此空间中Roy型奇偶非线性相干态是归一完备的, 但不具有正交性; 当复参数相位角θ满足一定条件时它们存在振幅平方压缩效应, 同时导出了压缩条件与参数s,r以及函数f(n)之间的关系. 最后借助于数值计算, 发现对于5维(或7维)Hilbert空间中Roy型偶(或奇)非线性相干态, 当参数θ和Lamb-Dike参数η取某一给定值时, 在参数r变化的不同取值范围内, 它们均可以呈现振幅平方 关键词： 有限维Hilbert空间 Roy型非线性相干态 奇偶非线性相干态 振幅平方压缩