Applications of quantum Fourier transform in photon-added coherent state

Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state （HTPACS）, which is obtained by letting the photon-added coherent state （PACS） across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate-momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.     

Construction of Laguerre polynomial's photon-added squeezing vacuum state and its quantum properties

Laguerre polynomial's photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial's photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of (a^1a^+). Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that,firstly, the squeezing effect of the 1-order Laguerre polynomial's photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter;secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and subPoissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial's photon-added operator on squeezing vacuum state can enhance its non-classical properties.     

Hermite Polynomial’s Photon Added Coherent State and its Non-classical Properties

In this paper, we will present the Hermite polynomial’s photon added coherent state (HPPACS), which can be obtained by superposing the photon-added coherent states(PACS) in the form of Hermite polynomial . Some quantum statistical properties of the introduced HPPACS, such as the Q-function, photon-number distribution, etc., are investigated. Meanwhile, we also give some profound squeezing properties of the HPPACS through its position distribution, quadrature squeezing and the degree of squeezing. Finally, the fidelity between the squeezed coherent state (SCS) and the HPPACS will be investigated numerically.     

Non-classical properties of the single-mode cavity field after interacting with a■-type three-level atom

<正>We study the non-classical properties of the single-mode electro-magnetic field resulting from the interaction of a S-type three-level atom initially in the coherent state,such as squeezing properties and sub-Poisson statistics.We show that if there are more photons in the cavity,the squeezing will appear earlier and be stronger under the same state,but the sub-Poisson statistics will be weaker,while sub-Poisson statistics and squeezing are more pronounced after the selective atomic measurement.     

Photon-Added SU(1, 1) Coherent States and their Non-Classical Properties

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

     

Study of higher order non-classical properties of squeezed Kerr state

Recently, Prakash and Mishra [J. Phys. B: at. Mol. Opt. Phys., 39, 2291(2006); 40, 2531(2007)] have studied higher order sub-Poissonian photon statistic conditions for non-classicality in the form of general inequalities for expectation values of products of arbitrary powers of photon number and of photon-number fluctuation. It is, therefore, vital to study the generation of these higher order sub-Poissonian photon statistics (phase-insensitive behavior) in a physically realizable medium and their relations to higher order squeezing (phase-sensitive behavior). In the present paper, we study higher order non-classical properties, such as Hong and Mandel squeezing, amplitude-squared squeezing and higher order sub-Poissonian photon statistics, of squeezed Kerr state which is generated by squeezing the output of a Kerr medium whose input is coherent light. Such states can be realized if laser light is sent through an optical fiber and then into a degenerate parametric amplifier. It is established that the squeezed Kerr state can exhibit higher order non-classical properties.     

Quantum Properties of the State via Operation of Superposition of Photon Subtraction Two Times and Photon Addition Two Times on Two Modes Squeezing Vacuum State

Superposition of photon subtraction two times and photon addition two times excited two modes squeezing vacuum state (SPSAESVT) is introduced, which is generated by operation of superposition of annihilation operator and creation operator on two modes squeezed vacuum state. Non-classical properties of SPSAESVT, such as squeezing effect, anti-bunching effect, the violation of Cauchy-Schwartze inequality and the entanglement property between two modes, are investigated. Using numerical methods, the influences of the superposition coefficient of operators and that of squeezing parameter on its non-classical properties are discussed. The results show that SPSAESVT does not display antibunching effect, but it displays squeezing effect, and there are the violation of Cauchy-Schwartze inequality and the entanglement between two modes. Further, its squeezing effect is not affected by the superposition coefficient of the operators, but there is a nonlinear relationship both between the violation of Cauchy-Schwartze inequality and the superposition coefficient, and between the entanglement property and the superposition coefficient. As squeezing parameter increases, its squeezing effect and entanglement property are strengthened, but the violation of Cauchy-Schwartze inequality is weakened.     

Nonclassicality Generated by Applying Hermite–Polynomials Photon-Added Operator on the Even/Odd Coherent States

We examine nonclassical properties of the quantum state generated by applying Hermite polynomials photon-added operator on the even/odd coherent state (HPECS/HPOCS). Explicit expressions for its nonclassical properties, such as quantum statistical properties and squeezing phenomenon, are obtained. It is interesting to find that the HPECS/HPOCS exhibits sub-Poissonian distribution, anti-bunching effects and negative values of the Wigner function. Thus, we confirm the HPPECS/HPPOCS is a new nonclassical state. Finally, we reveal that the HPPECS/HPPOCS is a novel intelligent state by its squeezing effects in position distribution and quadrature squeezing.     

拉盖尔多项式算符激发相干态的非经典性质

将拉盖尔多项式算符作用在相干态上,构造了拉盖尔多项式算符激发相干态.利用有序算符积分技术,导出了它的归一化系数以及〈a^la^+m〉的计算表达式.采用数值计算方法,讨论了相干态相位角和平均光子数对它的非经典性质的影响.研究结果表明:一阶拉盖尔多项式算符激发相干态呈现出压缩效应、反聚束效应、亚泊松分布和Wigner函数负性等量子特性,并且相干态的相位角对它的量子特性有重要影响;另一方面,随相干态平均光子数增大,它的反聚束效应和亚泊松分布性质逐渐减弱,压缩效应和Wigner函数的负性却先增强,而后又逐渐减弱.     

非经典态光场的判据

本文给出一个判别非经典态光场的普遍方法,由之仔细讨论了两类有实际意义的单模非经典态光场(反聚束光场和压缩态光场)的非经典实质。 关键词：     

双模最小关联混态的量子统计性质

研究了双模最小关联混态在不同参数情况下的量子统计性质.发现在一定的参数范围内双模最小关联混态的二阶相干性违反经典的Cauchy-Schwartz不等式,呈现非经典性相关;同时对双模最小关联混态的压缩特性、亚泊松分布等非经典性质进行了分析,通过数值计算得出,每模光子的压缩性及其亚泊松分布均与参数d的取值密切相关.     

Atomic transition transfer, field statistics and squeezing of the off-resonant cascade three-level Jaynes-Cummings model with a Kerr medium

Atomic population dynamics and the non-classical properties of the field in the system consisting of a cascade three-level atom interacting non-resonantly with a single-mode field are investigated in the presence of a Kerr medium. The atom and the field are assumed to be in the upper state and the coherent state initially, respectively. It is found that an atomic transition transfer may occur by varying the initial field intensity under the condition of a reasonably large one-photon detuning. Varying the initial field intensity can also control the field statistics. Quasiprobability distribution Q-function of the field state is also calculate to reveal its relation to the field statistics and normal squeezing effect.     

远程控制光场的量子统计性质

考虑双模纠缠相干光场,将其中一束光场注入腔中与一个二能级原子发生共振相互作用,总系统在腔量子电动力学演化过程中,对原子作选择性的测量,通过操纵参加相互作用的时间以及选择适当的光场参量可控制未参加相互作用光场的量子统计性质,在一定条件下可产生反聚束、压缩态等非经典光场,并且通过适当的控制和调整这些参量可以改变未参加相互作用光场的反聚束和压缩特性的强弱。这样,通过利用腔与原子之间简单的共振相互作用和相干光场之间的纠缠关联,实现了远程的、无直接量子测量的控制或改变相干光场的非经典性质这一目的。     

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     

Modified nonclassical coherent state: Squeezing,antibunching, sub-Poissonian photon statistics,realization scheme with the χ<Superscript>(2)</Superscript>-nonlinearity,and generation of a macroscopic entangled state

The nonlinear χ⁽²⁾ Mach-Zehnder interferometer is proposed as a device for conditional generation of a modified coherent nonclassical state. We show that the generated macroscopic state exhibits nonclassical effects, such as squeezing, photon antibunching, and sub-Poissonian statistics. The modified coherent state generates a macroscopic entangled state. The scheme works without the photon number resolving detection but requires high-efficiency photodetectors. We explain the mechanism of generation of the modified coherent non-classical state. The text was submitted by the author in English.     

极化激元系统时间演化的量子涨落特性和非经典统计行为

将极化激元系统约化成模型单模光子-TO声子有效相互作用系统， 在此基础上以解析形式讨论了系统的力学量、压缩态、量子涨落特性以及亚泊松分布等非经典效应的动力学演化行为.结果表明，光子场与极化波量子场彼此交换能量过程随时间演化呈振荡性质，光子场和声子场都可以演化成压缩态，其二阶压缩度随时间演化成复杂周期振荡特性，这种非经典特性是非线性相互作用的结果并且以k₁项和k₂项同时存在并相互关联为前提.而此时光子和声子统计分布随时间演化呈现介于超Poison分布和亚Poison分布之间复杂周期振荡的新结果，非线性作用k₁项和k₂项对这种非经典统计行为都有贡献. 关键词： 极化激元系统动力学演化 单模光场-TO声子有效模型哈密顿量 量子涨落与压缩态 亚泊松分布     

Odd-Excited Binomial States of the Radiation Field and Some of Their Statistical Properties

In this paper a new state called odd-excited binomial state (OEBS) is introduced. It interpolates between the odd number state and the odd-excited coherent state. We discuss some statistical properties, such as the Glauber second-order correlation function and squeezing phenomenon (normal and amplitude-squared squeezing) for this state. The quasiprobability distribution functions (Husimi Q-function and Wigner W-function) are also examined.     

超高斯纯态的一些性质

引入一种坐标概率密度分布介于高斯分布和矩形分布之间的量子力学纯态——超高斯纯态.研究了这种态的某些量子力学性质、压缩和高阶压缩以及Shannon熵等，并讨论了Shannon熵与压缩的关系. 关键词：     

实验条件不完美对薛定谔猫态制备的影响

薛定谔猫态是一类重要的非经典光场,实验上可以通过真空压缩态减光子的方案获得.本文从理论上研究了实验条件对制备薛定谔猫态的影响,主要考虑了包括压缩态的压缩度和纯度、单光子探测器的效率及噪声以及零拍探测器的效率等诸多因素的影响.理想情况下通过减光子方案制备得到的薛定谔猫态为奇光子数态,其相空间原点的Wigner函数为负值是其非经典特性的重要判据,而保真度可以度量制备态与理想猫态之间的相似程度.在压缩态为非纯态以及单光子探测器为商用低效率阈值探测器的情况下,计算了制备猫态的保真度、Wigner函数及其相空间原点处W（0）的表达式,分析了实验条件对薛定谔猫态制备的影响,为制备高质量的薛定谔猫态提供了理论指导.     

Four modes of optical parametric operation for squeezed state generation

We report a versatile instrument, based on a monolithic optical parametric amplifier, which reliably generates four different types of squeezed light. We obtained vacuum squeezing, low power amplitude squeezing, phase squeezing and bright amplitude squeezing. We show a complete analysis of this light, including a full quantum state tomography. In addition we demonstrate the direct detection of the squeezed state statistics without the aid of a spectrum analyser. This technique makes the nonclassical properties directly visible and allows complete measurement of the statistical moments of the squeezed quadrature.Received: 10 March 2003, Published online: 26 August 2003PACS: 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurementsU.L. Andersen: Present address: Institute of Optics, Information and Photonics, Max-Planck Research Group, University of Erlangen-Nuernberg, 91058 Erlangen, Germany.