共查询到20条相似文献,搜索用时 453 毫秒
1.
强调双模厄米多项式在量子光学理论中的地位,认为它是研究连续变量纠缠态和压缩态的必要函数,具有明确的物理意义。利用双模厄米多项式,结合有序算符内的积分技术,给出了若干新的算符恒等式和互逆的积分变换公式,证明了压缩双模粒子数态恰好是双变量厄米多项式激发压缩真空态。 相似文献
2.
《中国物理 B》2015,(10)
By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials.Its application in deriving the normalization for some quantum optical states is presented. 相似文献
3.
New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation
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By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration. 相似文献
4.
The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied. 相似文献
5.
SHAO Yu-Chong FAN Hong-Yi 《理论物理通讯》2008,49(4):866-870
For Hermite polynomials of radial coordinate operator in three-dimensional coordinate space we derive its normal ordering expansion, which are new operator identities. This is done by virtue of the technique of integration within an ordered product of operators. Application of the new formulas is briefly discussed. 相似文献
6.
《中国科学:物理学 力学 天文学(英文版)》2010,(9)
Dirac's ket-bra formalism is the language of quantum mechanics.We have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors in previous work.In this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite polynomials.This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way. 相似文献
7.
FAN Hong-Yi WANG Ji-Suo 《理论物理通讯》2007,47(4):611-616
Based on the bipartite entangled state representation and using the technique of integration within an ordered product (IWOP) of operators we construct the corresponding operator Fredholm equations and then derive their solutions. As its application we deduce some new bosonic operator identities and new relations about the two-variable Hermite polynomials. 相似文献
8.
FANHong-Yi 《理论物理通讯》2004,42(3):339-342
By virtue of the technique of integration within an ordered product of operators and the fundamental operator identity Hn(X)=2^n : X^n :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,: : is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermitc polynomials, but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → : f(X) :is also discussed. 相似文献
9.
10.
Hong-Yi FAN 《理论物理通讯》1994,21(4):509-512
By virtue of the technique ofintegration within an ordered product of operators we show that the ordinary Bargmann space basis function zn/√n! can be extended to two-variable Hermi te polynomials, the latter can span a generalized Bargmann space. The corresponding twomode Hermite polynomial states are thus introduced and their properties are investigated. 相似文献
11.
用文献[1]中提出的有序算符内的积分技术,简洁地导出了[量子光学学报,2002,8(1):8-12]一文中给出的有用的光场算符公式,并引入了双模厄米特多项式来表达这些公式. 相似文献
12.
Based on the technique of integration within an ordered product (IWOP) of operators we show that the operator ordering method
can lead us to derive new operator identities and new integration formulas regarding to Hermite polynomials.
Work supported by specialized research fund for the doctoral progress of higher education of China. 相似文献
13.
Based on the conclusion that the generalized Bargmann representation of a
two-mode Fock state is a two-variable Hermite polynomial function [Hong-Yi
Fan and Jun-hua Chen, Phys. Lett. A303 (2002) 311] we derive the generalized
Bargmann representation of the spin coherent state and some new relations in
the generalized function space. 相似文献
14.
In this paper, we provide a simple and neat approach to some operators’ normal ordering and antinormal ordering formulas in
quantum optics. Namely, we directly adopt the generating function of Hermite polynomial and the Baker-Hausdorff formula, which
differs from the existing ways. As an important byproduct, based on these operator identities, some useful mathematical integral
formulas are easily given without really performing these integrations. 相似文献
15.
With the help of technique of integration within an ordered product (IWOP) of operators we find new integration transformation connecting the coherent state and the biparticle entangled state. We also point out that under this kind of integration transformation the direct product of two single-variable Hermite polynomials behaves quite different from the two-variable Hermite polynomials, in this way we show that the latter is intrinsic to the phase space of quantum entanglement. As a byproduct, some operator identities for theoretical quantum optics can also be neatly expressed in terms of the two-variable Hermite polynomials. 相似文献
16.
By virtue of the technique of integration within Weyl ordered of operators we derive the formula of Weyl ordering expansion of power product of coordinate and momentum operators (√2Q)^m(√2iP) ^τ=:: Hm,r (√2Q, √2iP)::, the introduction of two-variable Hermite polynomial Hm,r brings much convenience to the study of Weyl correspondence. 相似文献
17.
18.
References: 《理论物理通讯》2007,47(6):1024-1028
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(γ)Hm,n (μa1^+, μa2^+│00〉, which is the minimum uncertainty state for sum squeezing, in ( η│representation is calculated. 相似文献
19.
New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states
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For directly normalizing the photon non-Gaussian states(e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product(IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering. 相似文献
20.
Based on the technique of integration within an ordered product of operators, we derive new bosonicoperators‘ ordering identities by using entangled state representation and the properties of two-variable Hermite poly-nomials H and vice versa. In doing so, some concise normally (antinormally) ordering operator identities, such asa man =:Hm,n(a ,a):, ana m = (-i)m n:Hm,n(ia ,ia): are obtained. 相似文献