Completeness Relation of the SU(3) Charged and Hypercharged Coherent State

Using the MelJin inversion formulas we derive the weight function for constructing the completeness relation of the boson SU(3) charged and hypercharged coherent state. A suitable contour integration is selected for this derivation.     

q-Analogue Charged Coherent State and SU(3) Charged,Hypercharged Coherent State

We generahe the conception of q-analogue coherent state to the cases of charged coherent state and charged, hypercharged coherent state. Their explicit expressions in the ordinary Fock space are derived.     

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：     

超导体中库珀对的SU(2)与Glauber相干态——库珀对与约瑟夫森超流性的量子特性研究

本文利用类自旋算符证明BCS超导基态波函数是单个库珀对SU(2)相干态波函数的直积、且在一定条件下为库珀对体系的SU(2)相干态波函数。若两块处在BCS超导基态的超导体耦合在一起,则体系仍处在SU(2)相干态,且在一定条件下为定态超辐射态。在SU(2)群到谐振子群的收缩下,库珀对的SU(2)相干态变为Glauber相干态。讨论了两种情形下库珀对与约瑟夫森超流性的量子噪声、分布及二阶相关特性。     

SU(1,1)相干态光场的统计特性及其对原子动力学行为的影响

研究了Ｂａｒｇｍａｎ指标为ｋ＝１／４和ｋ＝３／４的两种ＳＵ（１，１）相干态光场的特性，证明了两种相干态具有不同的量子统计特性，并讨论了光场初始处于ＳＵ（１，１）相干态时，双光子Ｊａｙｎｅｓ－Ｃｕｍｍｉｎｇｓ（Ｊ－Ｃ）模型中，原子的动力学行为及粒子数反转随时间的演化，证明了与初始一般相干态光场不同，原子展现出特殊的周期振荡和脉冲行为。 关键词：     

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     

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。     

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate of $\hat{K}_{-}^{2}The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schr?dinger cat states defined as an eigenstate of are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures.     

Coherent State Representations of Lie Superalgebra SU(2/1)

We present a kind of new coherent states associated with the Lie superalgebra SU(2/1), and discuss their properties in detail. We also evaluate the matrix elements of the SU(2/1) generators in the coherent state representations and obtain differential realizations of the SU(2/1) algebra in the coherent state space. The differential realizations may be useful for the study of the quasi-exactly solvable problems in the quantum mechanics.     

半导体中电子-空穴对的相干态、复合辐射和噪声压缩

本文讨论了在光的相干激发下,半导体中电子-空穴对的玻色近似和SU(2)相干态的产生,讨论了两种情形下电子-空穴对噪声特性和复合辐射特性,给出了电子-空穴对的二阶相干函数和分布函数,说明了玻色近似相当于SU(2)群到谐振子群的收缩。 关键词：     

Study of Concurrence and D-Concurrence on Two-QubitsResulted in Pair Coherent States in Language of SU(2) Coherent States

Pair coherent state, is a state of a two-mode radiation field that is known as a state with non-gaussian wave function. In this paper, study on the pair coherent state, we notice that with superposition of two first terms of this states, one two-qubits formed. Because of the importance of two-qubits in theory of quantum entanglement, with two different measures with the title of concurrence and D-concurrence, we have studied the amount of entanglement and
discussed its details. At the end, we describe these measures for pair coherent states as a function of the amplitude of the SU(2) coherent states.     

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。     

Enhancement of Sensitivity by Initial Phase Matching in SU(1,1) Interferometers

We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even(odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.     

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.     

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．     

Laguerre Polynomial States and Phase States in k-Photon Sub-Fock Space

Using k-photon Brandt-Greenberg operators we introduce the concept of field intensity-dependent squeezing, and construct the minimum uncertainty states for this squeezing,which turns out to be a Laguerre polynomial state in sub-Fock space. The k-photon phase states is also derived, which turns out to be an SU(1,1) generalized coherent state.     

Coherent states and quantum oscillations of BEC-BCS systems

We show by using the mean-field approximation that the states of composite Fermi-Bose superfluids created in cold-atom traps via a Feshbach resonance at zero temperature are generalized SU(2)⊗SU(1,1) coherent states. In response to a sudden change of the interaction between fermionic atoms and bosonic molecules, a Cooper pair can exhibit collapse and revival quantum behaviors for an initial generalized coherent state of molecules, and Rabi oscillation for a vacuum molecular state. Occurrence of the collapse and revival phenomenon is thus the manifestation of the formation of the Bose-Einstein condensate.     

利用原子-腔场的拉曼相互作用制备双模SU(2)薛定谔猫态

利用一个参量频率转换过程,在腔中制备双模ＳＵ（２）相干态,然后注入一个与腔场的一个个模发生拉曼相互作用的Ａ型三能级原子,通过原子－腔场相互作用生成腔场－原子纠缠,通过对原子进行选择性测量,腔场－原子纠缠态将塌缩到纯态,即双模ＳＵ（２）薛定谔猫态。     

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.

     

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.