SU(1,1)群的非齐次逆微分实现

利用玻色振子的逆算符构造了SU(1,1)群的生成元和不可约表示的相干态,导出了SU(1,1)群的非齐次逆微分实现.     

哈密顿算符是SU(1,1)和SU(2)算子含时线性组合量子系统的时间演变及厄密不变量

研究了哈密顿算符是SU(1,1)和SU(2)算子线性组合且系数显含时间量子系统的时间演化,我们发现适当选取厄密不变量,不仅可得到统一的量子态时间演化封闭解,而且可得到时间演化幺正算符。用时间演化算符我们讨论了含时双光子压缩态和SU(1,1)相干态以及SU(2)压缩态的压缩性质。     

SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

Two Kinds of Two-Boson Realizations of Generally Deformed Algebras with Three Generators

In this paper two kinds of two-boson realizations of generally deformed algebras with three generators are obtained by generalizing the Jordan-Schwlnger realizations of SU（2） and SU（1,1）. For each kind, a unitary realization and a non-unitary realizatlon, together with the properties of their acting spaces, are discussed. Similarity transformations that relate the non-unitary realizations to the unitary ones are given by solving unitarization equations.     

Two-Parameter Deformations of SU(2) and SU (1,l) Algebras

The algebras SU(2) and SU(1,1) are promoted to two-parameter quantum universal enveloping algebras (QUEA) by a doubleparameter deformation in this paper. The discrete unitary irreducible representations and their deformed coherent states are studied. The deformed generators are given by a Jordan-Schwinger realization and a Bargmann-Fock representation. It is also interesting that the two-parameter deformed coherent states are found to relate to the oneparameter deformed ones by a simple scaling transformation and this can be used to derive the completeness relation of the former.     

两参数变形量子代数SU(1,1)q,s的相干态及其性质

利用SU(1,1)_q,s量子代数的两参数变形振子构造出归一化的SU(1,1)_q,s相干态,证明了SU(1,1)_q,s量子代数的表示基是正交的,并讨论了它的相干态的归一性和完备性。指出(SU(1,1)_q,s相干态的相干性受参数q、s的影响。     

UNCORRELATED TWO-MODE SU(1,1) COHERENT STATES

We have constructed a new kind of two-mode bosonic realization of SU(1,1) Lie algebra, on the basis of which the SU(1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU(1,1) coherent states, which are called uncorrelated two-mode SU(1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy－Schwarz inequality and two-mode squeezing.     

Phase sensitivity of two nonlinear interferometers with inputting entangled coherent states

We investigate the phase sensitivity of the SU(1,1) interfereometer [SU(1,1)I] and the modified Mach–Zehnder interferometer(MMZI) with the entangled coherent states(ECS) as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU(1,1)I can beat the shot-noise limit(SNL) and approach the Heisenberg limit(HL). In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU(1,1)I, and the MMZI is more robust against internal photon losses than the SU(1,1)I.     

Quantum entanglement in the system of a moving V-type three-level atom interacting with the SU（1,1）-related coherent fields

In a system with a moving V-type three-level atom interacting with the SU(1,1)-related coherent fields, we investigate the entanglement between the moving three-level atom and the SU(1,1)-related coherent fields by using the quantum-reduced entropy, and that between the SU(1,1)-related coherent fields by using the quantum relative entropy of entanglement. It is shown that the two kinds of entanglement are dependent on the atomic motion and exhibit the periodic evolution with a period of 2π/p. The maximal atom--field qutrit entanglement state can be prepared, and the entanglement preservation of the SU(1,1)-related coherent fields can be realized in the interacting process via the appropriate selection of system parameters and interaction time.     

Exactly solvable models for atom-molecule Hamiltonians

We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.     

Hilbert-Space Representations of a Cross-Product Algebra Related to the 3D-Calculus on O(SU q (1,1))

Hilbert-space representations of the right cross-product *-algebra of the quantum SU(1,1) with a *-algebra related to Woronowicz's 3D-calculus on the quantum SU(1,1) are studied and classified.     

Maximally Entangled SU(1,1) Semi Coherent States

In this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.

     

Relationship Between Negative Binomial State and SU(1, l) Coherent State and Its q-Deformed Generalization

By choosing a suitable single-mode boson realization of SU(1,1) algebra we show that the associated SU(1,1) cohkrent state can be directly reformed as a negative binomial state. The q-deformed negative binomial state is introduced, and the relationship between this state and the SU_q(1,1) coherent state is also demonstrated.     

An SU(1,1) Boson Realization Involved in Solving the Three Coupled Harmonic Oscillators' Problem

We find that a three-mode boson realization of the SU(1,1) Lie algebra is involved in solving the three coupled harmonic oscillators' problem. Tire unitary operator U, which is found to be able to transform the Fock space of a three-dimcrrsional isotropic Irarmonic oscillator into the space in which the Hamiltonian of three coupled oscillators is diagonized, is further decomposed as a quantum-mechanical rotation in three-mode Hilbert space followed by an SU(1,1) squeezing transformation. The coordinate representation of this SU(1,1) unitary operator is obtained.     

叠加的奇偶SU(1,1)相干态的统计性质

研究了将两个SU(1,1)相干态｜ζ,k〉和｜ζ,k〉叠加起来得到的新的量子态的统计性质．偶SU(1,1)相干态｜ζ,1/4〉和奇SU(1,1)相干态｜ζ,3/4〉分别对应于压缩真空态和压缩单光子数态．适当选取SU(1,1)态的相位角和叠加时的相对相位,得到的新的量子态比单个SU(1,1)相干态表现出大大增强的正交分量压缩和光子反群聚效应．也说明了怎样准备这样的叠加态． 关键词：     

BCS Ground State and XXZ Antiferromagnetic Model as SU(2), SU(1,1) Coherent States: An Algebraic Diagonalization Method

An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL（2, C） and the Lorentz group via the Pauli grading （the elements of SL（2, C） expressed by direct sum of unit matrix and generators of SU（2） group）, we grade the SL（3,C） group with the generators of SU（3）, i. e. the Gell-Mann matrices, then express the SU（3） group in terms of three SU（2） subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL（2,C）. If the mapping from group SL（3,C） to the Lorentz group is constructed by choosing one SU（2） subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex -γμθ^μ is extended to encompass γ5γμθ^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.     

Generation of two-mode SU(2) and SU(1,1) cat states in a two-dimensional anisotropic ion trap

A scheme is proposed for generating two-mode SU(2) and SU(1,1) cat states for an ion trapped in a two-dimensional (2D) anisotropic harmonic potential trap. In the scheme the ion is excited by two laser beams in the trap plane. After an interaction time, a measurement on the internal state collapses the ion motion onto a superposition of two SU(2) or SU(1,1) coherent states depending on the laser frequencies. This work was supported by the National Natural Science Foundation of China under Grant No. 60008003, Fujian Provincial Natural Science Foundation of China under Grant Nos. K20004 and F0110027, and Funds from Fuzhou University.     

On the SU(3) Mass Formulae

It is found that in the SU(3) broken quark model the SU(3) generators and their time derivatives belong to the SU(3) × SU(3) algebra. Using this algebra and the infinite momentum method the SU(3) mass sum rules are obtained. The possibility is discussed that normal spin-parity nonets and anomalous ones differ in the structure of the mass spectrum.     

含G对费米子动力学对称SP(10)模型的Dyson玻色子实现

将费米子动力学对称模型包含G费米子对能够构造出SP(10)或SO(12)动力学对称群.本文用GeneralizedDyson玻色子映射方法求出SP(10)对称群精确的玻色子映像,其子群SU(5)生成元的玻色子映像与sdg相互作用玻色子模型(IBM)SU(5)生成元相同,唯象sdgIBMSU(5)极限能谱公式可由费米子动力学对称模型的微观参数描述.