Statistical Properties of the Generalized Photon-Added Pair Coherent State

We present a class of generalized photon-added pair coherent states (GPAPCS) and analyze some prominent nonclassical properties such as sub-Poissonian distribution and violations of Cauchy-Schwarz inequalities. In addition, we derive that the Wigner function of GPAPCS involves correlation of two two-variable Hermite polynomials and its Husimi function is related to a two-variable Hermite polynomial. Their behaviors varying with the phase space parameters are also graphically discussed. We find that the nonclassical effects of GPAPCS exhibits more with increasing of excitation photon numbers.     

热场动力学理论中的Husimi分布函数及Wehrl熵的研究

利用量子相空间技术和信息熵理论,研究了热场动力学理论中量子纯态与相应混合态的Husimi分布函数及Wehrl熵的一致性问题.结果表明,热相干态与相应混合态的Husimi分布函数及Wehrl熵完全相同,支持了热场动力学理论.且热相干态的Wehrl熵与平移因子无关,故在热相干态中,量子系统的可观测量的量子涨落及不确定关系也与平移因子无关.     

Spectral properties of chimera states

Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a spatiotemporal pattern of coherent and incoherent motion. We present here a detailed analysis of the spectral properties for such trajectories. First, we study numerically their Lyapunov spectrum and its behavior for an increasing number of oscillators. The spectra demonstrate the hyperchaotic nature of the chimera states and show a correspondence of the Lyapunov dimension with the number of incoherent oscillators. Then, we pass to the thermodynamic limit equation and present an analytic approach to the spectrum of a corresponding linearized evolution operator. We show that, in this setting, the chimera state is neutrally stable and that the continuous spectrum coincides with the limit of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.     

The Mth Coherent State

In this article, we propose a new kind of quantum states based on acting the number operator M times \( {\hat{n}}^M \) on the coherent state. We term this state the Mth coherent state, based on the value of the power M. We find that it is strongly similar to the coherent state as the analysis of the photonic statistical distributions and the overlap with the coherent state illustrate. Also, we find that it asymptotically reaches the minimum uncertainty and has a localized behavior in the Husimi function. However, in contrast to coherent state, the Mth coherent state has strong nonclassical features such as antibunching and squeezing for a relatively long range. Other parameters and measurements are discussed and studied. Finally, we highlight the similarity between the higher orders of the near coherent states and the Mth coherent states in order to potentially generate our proposed state.

     

Chaotic Eigenfunctions in Phase Space

We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions which is reminiscent of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on chaotic eigenconstellations, we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions for the constellations which fit quite well the chaotic data. We finally observe that specific dynamical information, e.g., the presence of high peaks (like scars) in Husimi densities, can be recovered from the knowledge of a few long-wavelength Fourier coefficients, which therefore appear as valuable order parameters at the level of individual chaotic eigenfunctions.     

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.     

New approach for solving the Wigner function from the Husimi function in the two-mode entangled state representation

We introduce a new method to calculate the Wigner function when its corresponding Husimi function is given. A new formula is derived for calculating conveniently the Wigner function in two-mode entangled state representation. As application, we derive Wigner functions of some quantum states, such as two-mode entangled state, the electron's two-mode squeezed canonical coherent state, and the electron's coordinate eigenstate.     

激发相干态在耗散量子通道中Husimi函数的演化

基于有序算符内的积分技术和量子力学相干态表象,本文研究了激发相干态在耗散量子通道中的Husimi函数的演化情况,首次推导了Husimi函数在耗散量子通道中的解析表达式,并通过绘制图形讨论了各种参数对Husimi函数的影响。     

量子相空间分布函数与压缩相干态表示间的变换关系

基于Husimi算符具有压缩相干态投影子形式, 首先介绍了一个新的量子算符表示, 即压缩相干态表示.当高斯展宽参数κ = 1时, 该函数约化为通常的P函数. 作为例子, 研究了热态的压缩相干态表示, 通过图示说明了压缩相干态表示与P函数的区别. 为更好地在量子光学问题中使用该表示, 我们揭示了压缩相干态表示与Wigner函数、Q函数以及Husimi函数间的积分变换关系.     

Wigner Function, Husimi Function and Tomogram of?Atomic?Coherent State as Energy Eigenstate of?Two?Coupled?Oscillators

In this work, we find that a set of energy eigenstates of the Hamiltonian of two coupled oscillators can be classified as the atomic coherent state in the Schwinger Bosonic realization. The statistical properties of these states are also discussed by analytically calculating their Wigner function, Husimi function and tomogram.     

Continuous variable quantum cryptography: beating the 3 dB loss limit

We demonstrate that secure quantum key distribution systems based on continuous variable implementations can operate beyond the apparent 3 dB loss limit that is implied by the beam splitting attack. The loss limit was established for standard minimum uncertainty states such as coherent states. We show that, by an appropriate postselection mechanism, we can enter a region where Eve's knowledge on Alice's key falls behind the information shared between Alice and Bob, even in the presence of substantial losses.     

New Application of Weyl Correspondence in Studying Husimi Operator

In this paper, the so-cMled Husimi operator △h（q,p; κ）, which is introduced by smoothing out the Wigner operator △ω（q,p） br averaging over the ＂coarse graining＂ function exp[-κ（q＇ - q）^2- （p＇- p）^2/κ], is now regarded as a Weft correspondence connecting the Husimi operator △h（q, p; κ） with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify ｜p, q; κ ） such that △ h （ q, p; κ ） = ｜p, q;κ ） （P, q; κ｜, where ｜P, q;κ） is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to tnd the Husimi operator is presented.     

Quasidistributions and coherent states for finite-dimensional quantum systems

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber–Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.     

Continuous‐variable quantum information processing

Observables of quantum systems can possess either a discrete or a continuous spectrum. For example, upon measurements of the photon number of a light state, discrete outcomes will result whereas measurements of the light's quadrature amplitudes result in continuous outcomes. If one uses the continuous degree of freedom of a quantum system for encoding, processing or detecting information, one enters the field of continuous‐variable (CV) quantum information processing. In this paper we review the basic principles of CV quantum information processing with main focus on recent developments in the field. We will be addressing the three main stages of a quantum information system; the preparation stage where quantum information is encoded into CVs of coherent states and single‐photon states, the processing stage where CV information is manipulated to carry out a specified protocol and a detection stage where CV information is measured using homodyne detection or photon counting.     

Wavelet Transformation and Wigner-Husimi Distribution Function

We find that the optical wavelet transformation can be used to study the Husimi distribution function in phase space theory of quantum optics. We prove that the Husimi distribution function of a quantum state |ψ〉 is just the modulus square of the wavelet transform of with ψ(x) being the mother wavelet up to a Gaussian function. Thus a convenient approach for calculating various Husimi distribution functions of miscellaneous quantum states is presented.     

Quasiprobability Distribution Functions of Squeezed Pair Coherent States

Using the entangled state representation of Wigner operator and some formulae related to the two-variable Hermite polynomials, the Wigner function of the squeezed pair coherent state (SPCS) and its two marginal distributions are derived. Based on the entangled Husimi operator introduced by Fan et al. (Phys. Lett. A 358:203, 2006) and the Weyl ordering invariance under similar transformations, we also obtain the Husimi function of the SPCS and its marginal distribution functions. The comparison between the two quasibability functions shows that, for the same amount of information included in two functions, the solving process of the Husimi function is simpler than that of the Wigner function. Work supported by the Natural Science Foundation of Shandong Province of China under Grant Y2008A23 and the Natural Science Foundation of Liaocheng University under Grant X071049.     

Representations of Canonical Commutation Relations Describing Infinite Coherent States

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.     

Coherent state polarons in quantum wells

We investigate the polaronic effects of an electron confined in a quantum well, which we describe through its algebraic properties using su(1,1), taking into account the electron-bulk longitudinal-optical phonon interaction. We construct the variational wave function as the direct product of an electronic part and a part describing coherent phonons generated by the Low–Lee–Pines transformation from the vacuum state. We use two explicit forms of coherent states, Perelomov and Barut-Girardello states, to represent the electronic part in the quantum well spectrum. Our results show that in a coherent state basis for electrons the basic polaron parameters such as the energy gap shift and effective mass are further enhanced compared to those obtained with the conventional sinusoidal form of the basis. The difference between the two types of quantum well coherent states appears in polaronic interactions in quantum wells. We extend the calculations in order to estimate polaron lifetimes for a variety of different material systems.     

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δ _h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ _h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 _{κ κ} 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ _h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution. Work supported by the National Natural Science Foundation under the grant: 10775097.