Two-Mode Excited Squeezed Vacuum State and Its Properties

In this paper, the two-mode excited squeezed vacuum state (TESVS) is studied by using the statistical method. By calculating the normalization of the TESVS, a new form of Jacobi polynomials and some new identities are obtained. The photon number distribution of the TESVS is given and it is a simple form of Jacobi polynomials. Using the entangled state representation of Wigner operator, the Wigner function of the TESVS is obtainded and the variations of the Wigner function with the parameters m, n, and r are discussed. Here from the phase space point of view the TESVS can be well interpreted and described.     

双模激发压缩真空态的维格纳函数

利用纠缠态表象下的维格纳(Wigner)算符,构造了双模激发压缩真空态的维格纳函数,并根据该函数在相空间ρ-γ中随参量m,n和r的变化关系,讨论了双模激发压缩真空态的量子干涉特性和压缩效应。结果表明,对于参量m,n不同的取值,双模激发压缩真空态的量子干涉效应的强弱不同;而对于不同的压缩参量r,双模激发压缩真空态呈现出不同程度的压缩效应。最后,根据双模激发压缩真空态的维格纳函数的边缘分布,阐明了此维格纳函数的物理意义。     

Husimi Functions of Excited Squeezed Vacuum States

Based on the Husimi operator in pure state form introduced by Fan et al., which is a squeezed coherent state projector, and the technique of integration within an ordered product （IWOP） of operators, as well as the entangled state representations, we obtain the Husimi functions of the excited squeezed vacuum states （ESVS） and two marginal distributions of the Husimi functions of the ESVS.     

Husimi Functions of Excited Squeezed Vacuum States

Based on the Husimi operator in pure state form introduced by Fan et al., which is a squeezed coherent state projector, and the technique ofintegration within an ordered product (IWOP) of operators, as well as theentangled state representations, we obtain the Husimi functions of theexcited squeezed vacuum states (ESVS) and two marginal distributions of theHusimi functions of the ESVS.     

用纠缠态表象讨论对双模压缩真空态作正交振幅分量的测量

对文献[4]的结果作了进一步推导,用纠缠态表象方法计算了对双模压缩真空态第一个模场作正交振幅分量测量的结果,发现第二个模塌缩到一个压缩态,其显式被导出。     

Husimi Function of Excited Squeezed Vacuum State

The q-p phase-space distribution function is a popular tool to study semiclassical physics and to describe the quantum aspects of a system. In this paper by using the pure state density operator formula of the Husimi operator Δ_h(q,p;κ)=|p,q〉_κκ〈p,q| we deduce the Husimi function of the excited squeezed vacuum state. Then we study the behavior of Husimi distribution graphically.     

激发压缩真空态的相位概率分布

应用Pegg和Barnett提出的相位算符和相位态理论,研究了激发压缩真空态的相位概率分布特性.数值计算结果表明,激发压缩真空态的相位概率分布主要受到相位参量和压缩参量的调节,相位参量使相位概率分布呈峰值结构,压缩参量的变化将影响相位概率分布的峰值强度,此外激发光子数对相位概率分布也有较大的影响.     

双模压缩数态光场的Wigner函数及其特性

借助纠缠态表象及Wigner算符在该表象下的表示,得到双模压缩数态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现双模压缩数态两模之间相互关联、相互纠缠,对相空间中Wigner函数分布产生影响. 关键词： 双模压缩数态 Wigner函数 纠缠态表象     

New Approach for Calculating Wigner Functions of Generalized Two-Mode Squeezed State and Squeezed Number State via Entangled State Representation

We construct the generalized squeezed vacuum state by virtue of the entangled state 〈η| [Fan Hongyi and J.R. Klauder, Phys. Rev. A47 (1994) 777] and derive the quantum fluctuation of the two-mode quadrature operators.We then calculate Wigner functions of the two-mode squeezed number states and generalized squeezing vacuum state in literature before.     

f-Deformed Squeezed Vacuum and First Excited States,Their Superposition and Corresponding Nonclassical Properties

In this paper, we introduce two new classes of nonlinear squeezed states that we name as f-deformed squeezed vacuum state|ξ, f even and f-deformed squeezed first excited state |ξ, f odd, which according to their production processes, essentially include only even and odd bases of Fock space, respectively. In the continuation, we introduce the superposition of these two distinct nonlinear squeezed states with a respective phase ?. Then, some of the criteria which imply the nonclassicality of the states, such as Mandel parameter, second-order correlation function, quadrature squeezing, amplitude-squared squeezing, Husimi and Wigner–Weyl quasi-distribution functions, are numerically examined. At last, by considering a well-known nonlinearity function associated with a nonlinear physical system, we present our results which outcome from the numerical calculations. It is shown that, the introduced f-deformed states can reveal high nonclassical features.     

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important properties of Wigner function for bipartite entangled systems, such as size of an entangled state, upper bound of Wigner functions, etc. These discussions demonstrate the beauty and elegance of the entangled state representation.     

双模压缩场与V型原子相互作用光场的性质

研究了双模压缩真空场与V型三能级运动原子的相互作用,得到光场二阶相干度和模间相干度的解析表达式;通过数值计算分析了原子运动速度、场模结构参数和平均光子数对光场二阶相干度和模间相干度的影响.结果表明:平均光子数的增加使得二阶相干度和模间相干度显著增大;而原子运动速度、模场结构参数的增加虽然对光子聚束效应和反聚束效应的强度影响不大,却使其演化周期大大减小.     

Applications of Weyl Ordered Two-Mode Wigner Operator for Quantum Mechanical Entangled System

Based on the technique of integral within a Weyl ordered product of operators, we present applications of the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.     

Evolution of a two-mode squeezed vacuum for amplitude decay via continuous-variable entangled state approach

Extending the recent work completed by Fan et al. [Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.     

Two-Variable Hermite Polynomial Excitation of Two-Mode Squeezed Vacuum State as Squeezed Two-Mode Number State

We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state （THPES）. We find that the Wigner function of THPES and its marginal distributions are just related to two-variable Hermite polynomials （or Laguerre polynomials） and that the tomogram of THPES can be expressed by one-mode Hermite polynomial.     

Casimir Force of Squeezed Vacuum

The Casimir force of the quantized electromagnetic field in the squeezed vacuum state is calculated betweena pair of parallel perfectly conducting plates at zero temperature.     

Entanglement Transfer from Two-Mode Squeezed Vacuum State Field to Two Spatially Separated Atoms in Two-Photon Processes

We investigate the influence of the Stark shift on the entanglement transfer from the two-mode squeezed vacuum state field to two spatially separated atoms in two-photon processes. Our results show that the Stark shift plays an important role in such entanglement transfer. We find that when the Stark shift parameter r is small, the degree of entanglement between the two atoms increases with the increasing of the squeezing parameter ξ first, and after achieving its maximal value, the degree of entanglement will decrease to zero with the increasing of ξ; while for big r, E will increase with the increasing of ξ.     

Casimir Force of Squeezed Vacuum

The Casimir force of the quantized electromagnetic field in the squeezed vacuum state is calculated between a pair of parallel perfectly conducting plates at zero temperature.     

双模压缩热态经过分束器前后的纠缠变化

本文采用对数负值来度量双模压缩热态通过分束器前后的纠缠属性的变化情况。结果表明,当输入对称双模压缩热态,无论如何调整分束器的相关参数,纠缠不会发生变化;而对于非对称双模压缩热态,在适当选择的分束器参数范围内,纠缠可能会发生变化。     

Properties of the q-Analogue of a Squeezed Vacuum State

We constructed a normalizable q-analogue of squeezed vacuum state using the technique of integration within an ordered product (IWOP) of operators and the properties of the inverses of q-deformed creation and annihilation operatots. We also study its nonclassical properties and phase probability distribution.