Operator properties of generalized coherent state systems

The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.     

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.     

Quantum Teleportation via Hybrid Entangled States

In this paper, we study quantum teleportation of atomic states via a hybrid entangled state (HES) involving an atom and a cavity field. And we investigate how to implement controlled phase (CP) gates between atomic internal states and coherent states of cavity field. We also discuss the methods of distinguishing coherent states |±α〉in a cavity. Finally, a brief discussion about the feasibility of this scheme in experiment is presented.     

宏观可分辨量子态的产生和检测

本文利用SO(3)旋转群性质得到了非线性双折射介质模型的一个严格解.由此证明相干态进入双折射介质后将产生宏观上可分辨的量子迭加态.为检测它们所产生的干涉条纹,本文采用零拍检测方案,计算了初态为线偏振和圆偏振相干光时零拍检测器输出流的几率分布.     

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter $p$ on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.     

制备囚禁冷离子的振动压缩量子态

基于非Lamb-Dicke近似下激光-离子相互作用的动力学规律,讨论了如何利用一系列的激光脉冲来驱动囚禁冷离子.从囚禁冷离子的运动基态出发获得压缩相干态、压缩奇偶相干态、压缩真空态等一系列的振动数态的叠加态.结果表明,只要适当地调节各个所用激光脉冲的长度和相位,总能很好逼近所需要的压缩量子态. 关键词： 囚禁冷离子 激光脉冲 压缩量子态     

有限维希尔伯特空间非简谐振子广义相干态

在有限维希尔伯特空间中构造了非简谐振子的广义相干态,并研究了其量子统计特性。详细地讨论了该量子态的压缩效应和反聚束效应,得到了出现压缩的条件并给陋了反聚束效应与有限维希尔伯特空间维数关系的数值计算结果。理论计算表明该量子态存在压缩效应和反聚束效应,这与通常的无限维空间中的广义相干态是完全不同的。     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

The quantum sling and the Schrödinger cat

The quantum sling is defined as a quantum harmonic oscillator with an abruptly vanishing frequency. It is shown in this article that a particle released by such a mechanism remains in acorrelated coherent state, i.e., a quantum state with the minimum dispersion in position and momentum allowed by the Schrödinger-Robertson uncertainty principle. This simple model permits to describe a Schrödinger-cat state (a quantum superposition of macroscopically distinguishable states) released by the sling. The result is a superposition of two correlated coherent states propagating in two opposite directions and with an interference term.     

Near-deterministic efficient all-optical quantum computation

We propose a flexible scheme to prepare various kinds of useful entangled coherent states using weak cross-Kerr nonlinearities and strong laser fields. We then show that, with such entangled states as off-line resources, near-deterministic quantum gates needed for coherent-state-based quantum computation can be efficiently implemented by means of in-line linear-optics elements.     

Classical breathers and quantum coherent states in discrete NLS systems

We present a comparison of quantum and “semiclassical” trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.     

Atomic Tunnelling Dynamics of Two Squeezed Bose-Einstein Condensates

In this paper, tunnelling dynamics of squeezed Bose-Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.     

A new class of quantum states generated by m-fold application of Bogoliubov＇s transformation

By applying higher powers of the Bogoliubov transformation operator b^{\dagger }=ν^*a+μ^*a^{\dagger } to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters λ and ρ, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.     

Comments on “Barut-Girardello Coherent States for the Parabolic Cylinder Functions”

In Chenaghlou and Faizy (Int. J. Theor. Phys. 2008), the authors claim that they have constructed the Barut-Girardello coherent states for the parabolic cylinder functions. However, we point out here that by introducing these coherent states, Schrödinger was able to put forth the idea of “coherent states of the quantum harmonic oscillator” over eighty years ago. These coherent states are derived not only from the Barut-Girardello eigenvalue equation, but also from the Schrödinger and the Klauder-Perelomov approaches. Thus, contrary to their claim, the authors have not introduced new coherent states. In particular, a wide range of the parabolic cylinder functions do not form an orthonormal basis.     

Transfer of quantum entangled states between superconducting qubits and microwave field qubits

Transferring entangled states between matter qubits and microwave-field (or optical-field) qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication. We here propose a way for transferring entangled states between superconducting qubits (matter qubits) and microwave-field qubits. This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities. Here, „qutrit” refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state. In contrast, the microwave-field qubits are encoded with coherent states of microwave cavities. Because the third energy level of each qutrit is not populated during the operation, decoherence from the higher energy levels is greatly suppressed. The entangled states can be deterministically transferred because measurement on the states is not needed. The operation time is independent of the number of superconducting qubits or microwave-field qubits. In addition, the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required. As an example, our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology. This proposal is quite general and can be extended to transfer entangled states between other matter qubits (e.g., atoms, quantum dots, and NV centers) and microwave- or optical-field qubits encoded with coherent states.     

Two-mode excited entangled coherent states and their entanglement properties

This paper introduces two types of two-mode excited entangled coherent states (TMEECSs) |Ψ_±(α,m,n)>, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state |Ψ₊(α,m,m)> the two-mode photon excitations affect seriously entanglement character while the state |Ψ_-(α,m,m)> is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.     

Generalized Photon Added and Subtracted f-Deformed Displaced Fock States

In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f-deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.     

通过Raman相互作用制备三个腔场的W型纠缠相干态

通过对比分立变量量子信息过程和连续变量量子信息过程的差别,利用相干态比较容易获得的这个特点,提出一种方案制备三个腔场的W型纠缠相干态.方案基于Λ型三能级原子与单模腔场的简并Raman 相互作用.三个相同的腔初始分别处于相干态,三个相同的原子初始处于W型纠缠态,通过三个原子分别与三个腔的Raman相互作用、选择适当的相互作用时间并探测作用后的三个原子,三个腔场坍缩为W型纠缠相干态.在原子与腔的相互作用过程中原子不处于高能级,可以忽略原子的自发辐射,系统的相干性能够得到较好的维持.基于当前的腔量子电动力学技术,相信方案能在实验上实现.该方案制备的三个腔场W型纠缠相干态有望在连续变量量子信息过程中有重要的应用价值.文中将方案推广到制备n(n〉3)个腔场的W型纠缠相干态.     

非Lamb-Dicke近似下制备囚禁冷离子的振动相干态

根据非Lamb-Dicke近似下激光-离子相互作用动力学规律,讨论了如何利用一系列的激光脉冲来驱动冷离子,从而从运动基态出发获得一系列振动数态的宏观叠加态.具体研究了这些叠加态的Q函数、Wigner函数和它们的非经典特性,如压缩和反群聚效应等.结果表明,合适地调节各个所用激光的脉冲长度,所产生的叠加态能很好地逼近熟知的振动相干态. 关键词： Lamb-Dicke近似 叠加态 相干态 非经典特性     

Study of Concurrence and D-Concurrence on Two-QubitsResulted in Pair Coherent States in Language of SU(2) Coherent States

Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and
discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU(2) coherent states.