Multi-Partite EPR Entangled State Representation for Continuous Variables and Its Application in Squeezing Theory

By extending the Einstein-Podolsky-Rosen (EPR) bipartite entanglement to an n-partite case, we construct the common eigenstate of the n-partite total coordinate and relative momenta for the continuous variables. The entanglement property of the state is shown. The classical dilation transform of variables in such a state induces a new n-mode squeezing operator related to an n-mode bosonic operator realization of SU(1,1) Lie algebra.     

Generation of Entangled Coherent States in Raman-Coupled Bose-Einstein Condensates

A method for producing entangled coherent states (ECSs) for atomic Bose-Einstein condensates (BECs) ispresented. The proposed method involves a BEC with three internal states and two classical laser beams ina three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulatingstrengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.     

Realization of Greenberg-Horne-Zeilinger （GHZ） and W Entangled States with Multiple Superconducting Quantum-Interference Device Qubits in Cavity QED

An alternative scheme is proposed for generating the Greenberg-Horne-Zeilinger （GHZ） and W types of the entangled states with multiple superconducting quantum-interference device （SQUID） qubits in a single-mode microwave cavity field. In this scheme, there is no transfer of quantum information between the SQUIDs and the cavity, the cavity is always in the vacuum and thus the requirement on the quality of cavity is greatly loosened. In addition, during the process of the generation of the W entangled state, the present method does not involve a real excitation of intermediate levels. Thus, decoherence due to energy relaxation of intermediate levels is minimized.     

Application of Y（sl（2）） Algebra for Entanglement of Two-Qubit System

We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y （sl（2） ） in quantum information.     

Construction of GHZ-Like States for a Three-Particle （Spin 1／2） System

As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of three-body operators of the form σασ2βσ3γ, the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with the irproduct being -1) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg-Horne-Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18 sets of partially entangled states, where only two particles are entangled.     

Generation of SU（2） Coherent States for a Cavity Mode and a Collective Atomic Mode

We propose a scheme for generation of SU（2） coherent states for an atomic ensemble and a cavity mode. In the scheme a collection of two-level atoms resonantly interact with a single-mode quantized field. Under certain conditions, the system can evolve from a Fock state to a highly entangled SU（2） coherent state. The operation speed increases as the number of atoms increases, which is important in view of deeoherence.     

EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra

We find that the Einstein-Podolsky-Rosen (EPR) entangled state representation describing bipartite kinematics is closely related to a new Bose operator realization of SU(2) Lie algebra. By virtue of the new realization some Hamiltonian eigenfunction equation can be directly converted to the generalized confluent equation in the EPR entangled state representation and its solution is obtainable. This thus provides a new approach for studying dynamics of angular momentum systems.     

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagationin GRIN media or some lens-setup.     

New Bose Operator Realization of SU(2) Algebra and Its Application in Optical Propagation

We introduce a new Bose operator realization of SU(2) Lie algebra and applied it to optical propagation in GRIN media or some lens-setup.     

双参数变形量子代数SU（1，1）_（q，s）的Nodvik实现和Holstein—Primakoff实现

给出了双参数变形量子代数ＳＵ（１，１）ｑ，ｓ的Ｎｏｄｖｉｋ实现和Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现，并给出了ＳＵ（１，１）ｑ，ｓ，和双参数变形振子的变形映射。     

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     

Generating Generalized Bessel Equations by Virtue of Bose Operator Algebra and Entangled State Representations

With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.     

SU(2)Thirring模型边界算子的Boson表达式

得到了有边界的SU(2)Thirring模型的反射矩阵Rab(θ),以及相应的边界算子的Boson表达式.     

Multi-mode Einstein-Podolsky-Rosen Entangled State Representation and Its Applications

Our primary purpose of this work is to explicitly construct the general multipartite Einstein-Podolsky-Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.     

导出双粒子纠缠态表象的新途径

对于量子光学的双粒子纠缠态表象,我们给出一个新途径以分析其在福克空间中的表达式.此分析自然导致双变数厄密多项式的引入,它截然不同于单变数厄密多项式.     

利用SU（2）_（q，s）量子代数的两参数变形振子实现讨论SU（2）_（q，s）相干态

利用ＳＵ（２）ｑ，ｓ量子代数的两参数变形振子实现构造出与Ｐｅｒｅｌｏｍｏｖ相干态形式不同的ＳＵ（２）ｑ，ｓ相干态．证明了ＳＵ（２）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（２）ｑ，ｓ相干态的相干性受参数ｑ，ｓ的影响，它比单参数变形ＳＵ（２）ｑ相干态更具一般性．