Multi-matrix vector coherent states

A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with multiple of quaternions and octonions are given. The resulting generalized oscillator algebra is briefly discussed. Further, vector coherent states for a tensored Hamiltonian system are obtained by the same method. As particular cases, coherent states are obtained for tensored Jaynes-Cummings type Hamiltonians and for a two-level two-mode generalization of the Jaynes-Cummings model.     

Schwinger boson mapping of SO(8) fermion model

The Schwinger representation of the SO(8) fermion pair algebra in terms ofd and quasispin vector (u, s, v) bosons is used in deriving a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the HFB variational solution. We can study the shape phase transition and pairing behaviour of the nuclear ground states using the coherent states.     

Vector coherent state theory for the S,D fermion pair algebra

The Ginocchio S,D fermion pair algebra is treated by vector coherent state theory to gain explicit matrix representations forthe physically relevant states of low S,D-pair generalized seniority for both the SO(8) ⊃ SO(6) × SO(2) and SO(7) ⊃ SO(5) × SO(2) branches. Although no boson approximations are necessary, vector coherent state theory is also used to give an exact, analytical s,d-boson realization of this fermion S,D-pair model.     

Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling

The propagation-dependent polarization vector fields are experimentally created from an isotropic microchip laser with a longitudinal-transverse coupling and entanglement of the polarization states. The experimental three-dimensional coherent vector fields are analytically reconstructed with a coherent superposition of orthogonal circularly polarized vortex modes. Each polarized component is found to comprise two Laguerre-Gaussian modes with different topological charges. With the analytical representation, the polarization singularities, on which the electric polarization ellipse is purely circular (C lines) or purely linear (L surfaces), are explored. The C line singularities are found to form an intriguing hyperboloidal structure.     

Kerr介质中双模SU(1,1)相干态场与V型三能级原子的相互作用

导出了充满Kerr介质的高Q腔中V型三能级原子与双模SU（1，1）相干态场相互作用系统的态矢量，并以此计算三能级原子布居概率和辐射场统计性质随时间的演化．数值计算显示，Ker效应产生与两能级原子不同的Rabi振荡特性，而双模场的关联特性受Kerr介质的影响较小．还讨论了Ker效应对Cauchy-Schwartz不等式的影响． 关键词：     

Classical particle in external Yang-Mills field and SU(2) coherent states

The relationship is indicated between a classical isospin vector for a classical particle in an external Yang-Mills field and SU(2) coherent states. The recipe for obtaining approximate isospin amplitudes from simple classical equations of motion is given.     

Observation of vector vortex lattices in polarization states of an isotropic microcavity laser

We experimentally investigate the formation of a vector polarization pattern from an isotropic microcavity laser. It is found that the orthogonal components of the observed pattern are localized on the geometrical rays. The connection between eigenfunctions and geometrical rays is analytically constructed by using the SU(2) coherent states. With the analytical function form, the observed vector pattern is completely reconstructed and the vector vortex lattice is apparent.     

有限维Hilbert空间Roy型奇偶非线性相干态的振幅平方压缩

构造出了有限维Hilbert空间Roy型奇偶非线性相干态, 讨论了它们的正交归一完备性和振幅平方压缩效应. 研究表明, 在此空间中Roy型奇偶非线性相干态是归一完备的, 但不具有正交性; 当复参数相位角θ满足一定条件时它们存在振幅平方压缩效应, 同时导出了压缩条件与参数s,r以及函数f(n)之间的关系. 最后借助于数值计算, 发现对于5维(或7维)Hilbert空间中Roy型偶(或奇)非线性相干态, 当参数θ和Lamb-Dike参数η取某一给定值时, 在参数r变化的不同取值范围内, 它们均可以呈现振幅平方 关键词： 有限维Hilbert空间 Roy型非线性相干态 奇偶非线性相干态 振幅平方压缩     

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。     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.     

Observation of spatially coherent polarization vector fields and visualization of vector singularities

We present experimental observations of polarization vector fields from a highly isotropic microchip laser with a large Fresnel number. The experimental polarization vector field leads to complex entanglement of spatial structures and polarization states. We theoretically derive the representation of generalized coherent states to reconstruct the experimental polarization-resolved patterns. The analytical and precise reconstruction enables the vector singularities to be clearly visualized.     

Evolution of Berry's phase in a graded-index medium

Evolution of the polarization vector in an inhomogeneous isotropic medium is investigated using the quantum-mechanical formalism of coherent states. The relation between the fluctuations of Berry's phase of wave nature caused by the “spin-orbit” interaction of a photon and depolarization of an incident pure state of polarization is clarified.     

A Categorical Framework for the Quantum Harmonic Oscillator

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures.     

Coherent States and Squeezed States in Interacting Fock Space

In this paper we study coherent states and squeezed states in one mode interacting Fock space.     

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

双模非经典光场辐照下介观约瑟夫森结中超流的动力学行为

研究了直流偏置电压下介观约瑟夫森结在SU（1，1）双模相干态光场作用下超流的动力学行为、流压台阶和直流分量等特性．研究发现超流能够呈现明显的崩塌与复苏现象，对于经典电磁场和非耦合的双模相干态光场作用下的情况，超流不出现此现象，且其流压台阶结构与后两种情况也不相同． 关键词：     

A Scheme for Teleportation of an Unknown Entangled Coherent State via Raman Interaction

A scheme is reported for the teleportation of entangled coherent states through the degenerate Raman interaction.The scheme uses an entangled state of an atom and two coherent states as a quantum channel.It makes full use of coherent cavity fields.Furthermore,it does not need any classical field to transform the atom states.     

Decoherence and Fidelity in Teleportation of Coherent Photon-Added Two-Mode Squeezed Thermal States

We theoretically introduce a kind of non-Gaussian entangled resources, i.e., coherent photon-added two-mode squeezed thermal states (CPA-TMSTS), by successively performing coherent photon addition operation to the two-mode squeezed thermal states. The normalization factor related to bivariate Hermite polynomials is obtained. Based upon it, the nonclassicality and decoherence process are analyzed by virtue of the Wigner function. It is shown that the coherent photon addition operation is an effective way in generating partial negative values of Wigner function, which clearly manifests the nonclassicality and non-Gaussianity of the target states. Additionally, the fidelity in teleporting coherent states using CPA-TMSTS as entangled resource is quantified both analytically and numerically. It is found that the CPA-TMSTS is an entangled resource of high-efficiency and high-fidelity in quantum teleportation.