New Bosonic Operator Ordering Identities Gained by the Entangled State Representation and Two-Variable Hermite Polynomials

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.     

Simple approach to deriving operator identities and mathematical formulas regarding to two-variable Hermite polynomials

By virtue of operator ordering technique and the generating function of polynomials, we provide a simple and neat approach to studying operator identities and mathematical formulas regarding to two-variable Hermite polynomials, which differs from the existing mathematical ways. We not only derive some new integration formulas and summation relations about two-variable Hermite polynomial, but also draw a conclusion that two-variable Hermite polynomial excitation of two-mode squeezed vacuum state is a squeezed two-mode number state. This may open a new route of developing mathematics by virtue of the quantum mechanical representations and operator ordering technique.     

Weyl Ordering Expansion of Power Product of Coordinate and Momentum Operators

By virtue of the technique of integration within Weyl ordered of operatorswe derive the formula of Weyl ordering expansion of power product ofcoordinate and momentum operators (2^1/2Q)^m (2^1/2iP )^r=::H_m,r(2^1/2Q,2^1/2iP ) ::, the introduction of two-variable Hermite polynomial H_m,r brings much convenience to the study of Weyl correspondence.     

量子力学坐标-动量算符幂次排序互换的简捷公式与新推导方法

量子力学坐标-动量算符幂次排序的相互转换是一个基本的量子力学课题, 本文提出了一个十分简捷有效的方法处理此问题, 即利用双变量厄米特多项式的母函数性质及有序算符记号内的算符特点, 给出一系列关于坐标-动量算符幂次排序的恒等式, 它们具有广泛的应用.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative： the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our mode/with the mode/ introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 （2002） 228301], it is proved that they are not in the same universality class.     

Two-Variable Hermite Polynomial Excitation of Two-Mode Squeezed Vacuum State as Squeezed Two-Mode Number State

We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state （THPES）. We find that the Wigner function of THPES and its marginal distributions are just related to two-variable Hermite polynomials （or Laguerre polynomials） and that the tomogram of THPES can be expressed by one-mode Hermite polynomial.     

Operators’s-parameterized ordering and its classical correspondence in quantum optics theory

In reference to the Weyl ordering xmpn→(1/2)mΣι=0m(ιm)Xm-ιPnXι , where X and P are coordinate and momentum operator, respectively, this paper examines operators’s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence ((1-s)/2)(n+m)/2Hm,n((2/(1-s))～(1/2)α,(2/(1-s))～(1/2)α)→a+man,and its complementary relation αnα*m→(-i)n+m((1-s)/2)(m+n)/2:Hm,n(i(2/(1-s))～(1/2)a+,i((2/(1-s))～(1/2)a):,where H m,n is the two-variable Hermite polynomial, a, a+ are bosonic annihilation and creation operators respectively, s is a complex parameter. The s’-ordered operator power-series expansion of s-ordered operator sa+mans in terms of the two-variable Hermite polynomial is also derived. Application of operators’s-ordering formula in studying displaced-squeezed chaotic field is discussed.     

Generation of squeezed TEM01 modes with periodically poled KTiOPO4 crystal

Spatial quantum optics and quantum information based on the high order transverse mode are of importance for the super-resolution measurement beyond the quantum noise level. We demonstrated experimentally the transverse plane TEM01 Hermite-Gauss quantum squeezing. The squeezed TEM01 mode is generated in a degenerate optical parametric amplifier with the nonlinear crystal of periodically poled KTiOPO4. The level of 2.2-dB squeezing is measured using a spatial balance homodyne detection system.     

A New Kind of Two-Fold Integration Transformation in Phase Space and Its Uses in Weyl Ordering of Operators

We propose a new two-fold integration transformation in p-q phase space∫∫^∞-∞dpdq/π e^2i（p-x）（q-y）f（p,q）≡G（x,y）,which possesses some well-behaved transformation properties. We apply this transformation to the Weyl ordering of operators, especially those Q-P ordered and P-Q ordered operators.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions＇ Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

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.     

Weyl Ordering Operator Formula Derived by IWOP Technique and Its Application for Fresnel Operator

Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators＇ Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Eresnel transformation kernel in classical optics.     

Nonclassicality of a two-variable Hermite polynomial state

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.     

First-principles study of orbital ordering in cubic fluoride KCrF_3

Comprehensive first-principles calculations are performed to provide insight into the intriguing physical properties of the ternary cubic fluoride KCrF3. The electronic structures exhibit a prominent dependence on the effective local Coulomb interaction parameter Ueff. The ground state of the cubic phase is a ferromagnetic （FM） half-metal with Ueff equal to 0, 2, and 4 eV, whereas the insulating A-type antiferromagnetic （A-AFM） state with concomitant homogeneous orbital ordering is more robust than the FM state for Ueff exceeding 4 eV. We propose that the origin of the orbital ordering is purely electronic when the cooperative Jahn-Teller distortions are absent in cubic KCrF3.     

基于纠缠态表象和自旋相干态的新复变函数空间

本文利用有序算符内的积分(IWOP)技术,构造了一个基于单变量厄米多项式H2j(ξ*+τξ/2√τ)的新复变函数空间,该空间与纠缠态表象及施温格玻色环境下的自旋相干态有关。推导出了包含二元厄米多项式的二项式定理,有助于构造新的复变函数空间。同时还提出了一种新的基于H2j(ξ*+τξ/2√τ)的积分变换及其逆变换,这对于推导某些算符恒等式是很有用的。     

Charge ordering modulations in a Bi0.4Ca0.6MnO3 film with a thickness of 110 nm

The low temperature sample stage in a transmission electron microscope is used to investigate the charge ordering behaviours in a Bi0.4Ca0.6MnO3 film with a thickness of 110 nm at 103 K. Six different types of superlattice structures are observed using the selected-area electron diffraction （SAED） technique, while three of them match well with the modulation stripes in high-resolution transmission electron microscopy （HRTEM） images. It is found that the modulation periodicity and direction are completely different in the region close to the Bi0.4Ca0.6MnO3/SrTiO3 interface from those in the region a little further from the Bi0.4Ca0.6MnO3/SrTiO3 interface, and the possible reasons for this are discussed. Based on the experimental results, structural models are proposed for these localized modulated structures.     

Some Properties of Two-mode Displaced Excited Squeezed Vacuum States

In this paper, two-mode displaced excited squeezed vacuum states （TDESVS） are constructed and their normalization and completeness are investigated. Using the entangled state representation and Weyl ordering form of the Wigner operator, the Wigner functions of TDESVS are obtained and the variations of Wigner functions with the parameters m, n and r are investigated. Besides, two marginal distributions of Wigner functions of TDESVS are obtained, which exhibit some entangled properties of the two-particle＇s system in TDESVS.     

Physics picture from neutron scattering study on Fe-based superconductors

Neutron scattering, with its ability to measure the crystal structure, the magnetic order, and the structural and magnetic excitations, plays an active role in investigating various families of Fe-based high-T c superconductors. Three different types of antiferromagnetic orders have been discovered in the Fe plane, but two of them cannot be explained by the spin-density-wave (SDW) mechanism of nesting Fermi surfaces. Noticing the close relation between antiferromagnetic order and lattice distortion in orbital ordering from previous studies on manganites and other oxides, we have advocated orbital ordering as the underlying common mechanism for the structural and antiferromagnetic transitions in the 1111, 122, and 11 parent compounds. We observe the coexistence of antiferromagnetic order and superconductivity in the (Ba,K)Fe 2 As 2 system, when its phase separation is generally accepted. Optimal T c is proposed to be controlled by the local FeAs 4 tetrahedron from our investigation on the 1111 materials. The Bloch phase coherence of the Fermi liquid is found crucial to the occurrence of bulk superconductivity in iron chalcogenides of both the 11 and the 245 families. Iron chalcogenides carry a larger staggered magnetic moment ( 2 μ B /Fe) than that in iron pnictides ( 1 μ B /Fe) in the antiferromagnetic order. Normal state magnetic excitations in the 11 superconductor are of the itinerant nature while in the 245 superconductor the spin-waves of localized moments. The observation of superconducting resonance peak provides a crucial piece of information in current deliberation of the pairing symmetry in Fe-based superconductors.     

New Integration Transformation Connecting Coherent State and Entangled State

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.     

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.