关于压缩态光场的教学

在激光物理课中,通常是从理论上定义压缩态|β>: |β>=S(ξ)|α> 其中S为压缩算符,ξ为压缩参量,|α>为相干态.然后证明|β>是光子压缩湮没算符b的本征态,求出正交相位(?)、(?)中(?)(θ_x)被压缩了.我们改变为从实验出发,引进b=μa+γa~+,说明相干态光场经过变换,产生了压缩态光场。这种变换     

两多模泛函相干态叠加态的高次和压缩--广义磁场分量的不等幂次高次和压缩效应

利用多模压缩态理论,研究了多模泛函相干态|{fj(x,y,z)}〉q及其相反态|{-fj(z,y,z)}〉q的线性叠加所组成的两态叠加多模叠加态光场|ψ(2)(f)〉q的广义磁场分量的不等幂次高次和压缩特性.结果发现:1)当各模的压缩次数Nj(j=1,2,…,…,q下同)之和为偶数时,态|ψ(2)(f)〉q恒处于不等幂次Nj-H最小测不准态;2)当各模的压缩次数Nj之和为奇数时,态|ψ(2)(f)〉q在一定条件下可呈现出周期性变化的、任意不等幂次的广义非线性高次和压缩效应.     

4个多模泛函相干态叠加态的等幂偶次Y压缩

构造了由多模泛函相干态|{fj(xj,yj,zj)}〉q、多模泛函相干态的相反态|{-fj(xj,yj,zj)}〉q、多模复共轭泛函相干态|{f j(xj,yj,zj)}〉q四态线性叠j(xj,yj,zj)}〉q和多模复共轭泛函相干态的相反态|{-f 加组成的四态叠加多模泛函叠加态光场|Ψ(4)(fj)〉q。利用多模压缩态理论,研究了态|Ψ(4)(fj)〉q的广义非线性等幂偶次Y压缩特性。结果表明:在一定条件下,态|Ψ(4)(fj)〉q可呈现出任意偶数次的广义非线性等幂次2p(p=1,2,…)次方Y压缩效应;光场经典强度的空间分布函数|fj(xj,yj,zj)|2(j=1,2,…,q),对态|Ψ(4)(fj)〉q的等幂偶次Y压缩效应的压缩程度、压缩深度和压缩幅度等产生直接影响。     

耦合二能级双原子与压缩光场相互作用平均光子数的演化

采用相互作用绘景,利用全量子化方法研究了压缩相干态光场与两个耦合二能级原子相互作用过程中,光子统计演化的规律;讨论了光场的压缩因子γ,相干振幅分量模平方|α|2、原子-场的耦合系数λ和原子间的耦合系数g对受激辐射场的平均光子数〈n(t)〉的影响,并揭示了它们之间的联系.     

α^2M本征态的偶奇表示形式

研究了光子湮没算符不同次幂αN的本征态，发现对于N为偶数的情况，αN的本征态可用α(N／2)的本征态表示成偶奇结构的形式;对于N为奇数的本征态，则没有相应的表示。由此对αN本征态的压缩特点进行了解释。     

压缩真空的特性

压缩真空S(r)|0〉是光的一种压缩态。本文讨论 了压缩真空的场强、位相、粒子数以及它们的涨落。由〈E〉=0〈cosφ〉=0可知压缩真空是位相混沌态。并且由〈E~2〉=〈E_+〉+〈E_-〉=1/2E_0(e~(2r)+e~(-2r))知一个分量被压缩另一分量膨胀,压缩分量的     

a~3正交归一本征态的高阶压缩

本文研究了光子消灭算符三次幂a~3正交归一本征态的高阶压缩。结果表明,a~3的三个正交归一本征态都没有Zhang等人定义的高阶压缩,但它们都是算符Z_1(N)和Z_2(N)(N=3m,m=1,2,…)的最小测不准态,从而推广了其他作者的结果。     

双模纠缠相干光场与Bell态原子相互作用系统的原子偶极压缩效应

运用解Schr(o)dinger方程和数值计算方法,研究了处于Bell态的两个全同二能级纠缠原子与双模纠缠相干光场相互作用系统的原子偶极压缩特性.分析了原子体系的初态、双模纠缠相干光场的纠缠程度、初始光场的平均光子数以及两纠缠原子的相互作用强度对偶极压缩性质的影响.结果表明:若初始时刻原子处在Bell态|β00〉、|β01〉和β11〉时,不会出现偶极压缩效应.而处在Bell态|β10〉时在一定条件下可呈现原子偶极压缩效应,且偶极压缩效应与初始光场的平均光子数和双模纠缠相干光场的纠缠程度有关.     

Kerr介质中V型三能级原子与压缩相干态光场相互作用系统Mandel因子的演化特性

研究了在充满Kerr介质的高Q腔中V型三能级原子与压缩相干态光场相互作用系统Mandel因子Q(t)的时间演化规律；讨论了Kerr介质强度系数μ、光场压缩因子γ、光场相干振幅分量模平方|α|^2。和原子-场的耦合系数λ对光子统计分布特性的影响。结果发现：μ、γ、|α|^2和λ都影响了Mandel因子Q(t)演化曲线量子崩塌-复苏效应的周期性，同时，也影响了受激辐射场的光子统计分布的状态和特性。     

激发双模SU(2)相干态的非经典性质

构造了激发双模SU(2)相干态|M,ξ;m〉=AMξma mb m|M,ξ〉,并用数值方法研究其非经典特性.结果表明,在双模SU(2)相干态的两场模同时增加光子后,两模光场仍然保持反关联特性,而且可以使光场对Cauchy-Schwartz不等式的破坏程度、光场的反聚束效应以及光子统计亚泊松分布等非经典特性得到加强.     

Hypothesis testing of complex covariance matrices

Letcal ybe a mean zero complex stationary Gaussian signal process depending on a vector parametertheta prime = { theta_{1}, theta_{2}, theta_{3} }whose components represent parameters of the covariance function R(r) ofcal y. These parameters are chosen astheta_{1} = R(0), theta_{2} = |R( tau )| /R(0), theta_{3} =phase ofR( tau), and they are simply related to the parameters of the spectral density ofcal y. This paper is concerned with the determination of most powerful (MP) tests that distinguish between random signals having different covariance functions. The tests are based uponNcorrelated pairs of independent observations oncal y. Although the MP test that distinguishes betweentheta = theta_{o}and the alternative hypothesistheta = theta_{1}has been solved previously [11], the problem of identifying the random signals is often complicated by the fact that the signal powertheta_{1} = R(0)is not a distinguishing feature of either hypothesis. This paper determines the MP invariant test that delineates between the composite hypothesislambda equiv R( tau)/R(0) = lambda_{0}and the composite alternativelambda = lambda_{1}. In addition, the uniformly MP invariant test that distinguishes between the composite hypothesestheta_{2} <_{=} | lambda_{o} |andtheta_{2} > | lambda_{0} |has also been found. In all cases, exact probability distributions have been obtained.     

The Dependence of Reflection on Incidence Angle

A Iossy dielectric sheet has complex dielectric constant epsilon = epsilon (x) and complex permeability µ = µ(x), where x is the distance to one interface. This sheet is backed by a conducting surface and used as an absorber. If | epsilon (x)µ(x) | >>epsilon/sub 0/µ/sub 0/, so that (epsilon/epsilon/sub0/)(µ/µ/sub0/) - sin² theta is nearly independent of the incidence angle theta, then the amplitude reflection R(theta) is wholly determined by R(0). Typical results: When R(theta/sub0/) = 0 at one polarization, then at theta=theta/sub 0/ the reflection for the other polarization corresponds to a voltage standing-wave ratio SWR =sec² theta/sub 0/. At perpendicular polarization max | R(theta) | on (theta/sub 1/, theta/sub 2/) is least, for given | R(0) I, if R(0) is real and positive; and then R(theta) = 0 at tan²theta/2 = R(0). But for parallel polarization R(0) must be real and negative to get optimum performance. When the absorber functions at both polarizations the best obtainable result is | R(theta) | = tan²theta/2, no matter what interval (theta/sub 1/, theta/sub 2/) is specified. The error in the approximation is investigated theoretically and experimentally. A complete set of graphs is included, suitable for design of those absorbers to which the theory applies. The analysis also yields an exact expression for the limiting behavior of the reflection at grazing incidence. This can be used in problems such as computation of the field due to a dipole over a plane earth. Finally, the theory of the Salisbury screen is re-examined as an aid in checking the other developments.     

BIBO Stability of D-Dimensional Filters

Consider the class of d-dimensional causal filters characterized by a d-variate rational function analytic on the polydisk . The BIBO stability of such filters has been the subject of much research over the past two decades. In this paper we analyze the BIBO stability of such functions and prove necessary and sufficient conditions for BIBO stability of a d-dimensional filter. In particular, we prove if a d-variate filter H(z) analytic on has a Fourier expansion that converges uniformly on the closure of , then H(z) is BIBO stable. This result proves a long standing conjecture set forth by Bose in [3].     

Erasure, list, and detection zero-error capacities for low noiseand a relation to identification

For the discrete memoryless channel (χ, y, W) we give characterizations of the zero-error erasure capacity C_er and the zero-error average list size capacity C_al in terms of limits of suitable information (respectively, divergence) quantities (Theorem 1). However, they do not “single-letterize.” Next we assume that χ⊂y and W(x|x)>0 for all x∈χ, and we associate with W the low-noise channel W_ϵ, where for y ⁺(x)={y:W(y|x)>0} W_ϵ(y|x)={1, if y=x and |y⁺(x)|=1 1-ϵ, if y=x and |y⁺(x)|>1 e/|y ⁺(x)|-1, if y≠x. Our Theorem-2 says that as ε tends to zero the capacities C_er(W_ε) and C_al (W_ε) relate to the zero-error detection capacity C _de(W). Our third result is a seemingly basic contribution to the theory of identification via channels. We introduce the (second-order) identification capacity C_oid for identification codes with zero misrejection probability and misacceptance probability tending to zero. Our Theorem 3 says that C_oid equals the zero-error erasure capacity for transmission C_er     

Determination of quantization error in two-dimensional digital filters

The evaluation of the quantization error in two-dimensional (2-D) digital filters involves the following computation J = Σm=0^∞Σn=0^∞y²(m, n). In this paper general method for the evaluation of J based on Laurent expansion of the integrand is presented. Illustrative example for such a computation is given. Notations: We denote with V^-2= {(z1, z2): |z1| ≤ 1, |z2| ≤ 1} the closed unit bidisc, with V²= {(z1, z2): |z1| < 1, |z2| < 1} the open unit bidisc, and with T2= {(z1, z2): |z1| = 1, |z2| = 1} the distinguished boundary of the unit bidisc.     

Investigation of the effect of frustration on the critical properties of the 3D Heisenberg antiferromagnetic model

The critical properties of the 3D frustrated Heisenberg model on a layered triangular lattice with a variable interlayer exchange interaction are investigated for the ratio of the constants of the interlayer (J′) and intralayer ( J ) interactions that ranges within the interval R = | J′/J| = 0.01…1. The finite-dimensional scaling theory is applied for the calculation of all of the main static magnetic and chiral critical indexes. It is shown that the 3D frustrated Heisenberg model on a layered triangular lattice forms a new universality class of critical behavior. It is found that the universality class of this model’s critical behavior is retained for values of R as small as R = 0.05.     

The Kolmogorov complexity, universal distribution, and codingtheorem for generalized length functions

A function h(w) is said to be useful for the coding theorem if the coding theorem remains to be true when the lengths |w| of codewords w in it are replaced with h(w). For a codeword w=a₀a₁...a_m-1 of length m and an infinite sequence Q=(q₀, q₁, q₂, ...) of real numbers such that 0n⩽½, let |w|_Q denote the value Σ_n=0^m-1 (if a_n =0 then -log₂q_n, else -log₂(1-q _n)), that is, -log₂, (the probability that flippings of coins generate x) assuming that the (i+1)th coin generates a tail (or 0) with probability q_i. It is known that if 0n→∞ q_n then |w|_Q is useful for the coding theorem and if lim_n→∞ q _n/(1/(2ⁿ))=0 then |w|_Q is not useful. We introduce several variations of the coding theorem and show sufficient conditions for h(w) not to be useful for these variations. The usefulness is also defined for the expressions that define the Kolmogorov complexity and the universal distribution. We consider the relation among the usefulness for the coding theorem, that for the Kolmogorov complexity, and that for the universal distribution     

No-Reference Video Quality Assessment using novel hybrid features and two-stage hybrid regression for score level fusion

This paper presents a novel No-Reference Video Quality Assessment (NR-VQA) model that utilizes proposed 3D steerable wavelet transform-based Natural Video Statistics (NVS) features as well as human perceptual features. Additionally, we proposed a novel two-stage regression scheme that significantly improves the overall performance of quality estimation. In the first stage, transform-based NVS and human perceptual features are separately passed through the proposed hybrid regression scheme: Support Vector Regression (SVR) followed by Polynomial curve fitting. The two visual quality scores predicted from the first stage are then used as features for the similar second stage. This predicts the final quality scores of distorted videos by achieving score level fusion. Extensive experiments were conducted using five authentic and four synthetic distortion databases. Experimental results demonstrate that the proposed method outperforms other published state-of-the-art benchmark methods on synthetic distortion databases and is among the top performers on authentic distortion databases. The source code is available at https://github.com/anishVNIT/two-stage-vqa.     

An on-line universal lossy data compression algorithm viacontinuous codebook refinement .III. Redundancy analysis

For pt.II see ibid., vol.42, p.822-36 (1996). The Gold-washing data compression algorithm is an adaptive vector quantization algorithm with vector dimension n. In this paper, a redundancy problem of the Gold-washing data compression algorithm is considered. It is demonstrated that for any memoryless source with finite alphabet A and generic distribution p and for any R>0, the redundancy of the Gold-washing data compression algorithm with dimension n (defined as the difference between the average performance of the algorithm and the distortion-rate function D(p,R) of p) is upper-bounded by |_δR /^δD(p,R)|((|A|+2ξ+4 log n)/2n)+σ(logn/n) where _δR/^δD(p,R) is the partial derivative of D(p,R) with respect to R, |A| is the cardinality of A, and ξ>0 is a parameter used to control the threshold in the Gold-washing algorithm. In connection with the results of Zhang, Yang, and Wei (see ibid., vol.43, no.1, p.71-91, 1997) on the redundancy of lossy source coding, this shows that the Gold-washing algorithm has the optimal convergence rate among all adaptive finite-state vector quantizers     

傅立叶级数展开式直流项的计算问题

在连续周期信号的傅立叶级数展开式中,很多文献普遍采用a0=an|n=0和c0=n|n=0来计算a0和c0间接得到其直流项.本文用一些具体例题分析说明了上述做法的矛盾,得出结论:用傅立叶级数法计算直流项在一些情况应该使用a0和c0各自独立的计算公式,而不应该用an和cn代入零来进行计算.