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.     

Statistical Properties of the nonlinear SU（1,1） Coherent States

Using non-Hermitian realizations of SU(1,1) Lie algebra in terms of an f-oscillator,we generalize the notion of nonlinear coherent states to the single-mode and two-mode nonlinear SU(1,1) coherent states.Taking the nonlinearity function f(k)=Lk^1(η^2)[(k 1)Lk^0(η^2)]^-1,their statistical properties are studied.     

Generation of SU(1,1) Intelligent States for the Motion of Two Trapped Ions

We propose a method for generating SU (1, 1) intelligent states for the center of mass and relative motionalmodes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the sameas the direction of the two trapped ions‘ alignment. Under certain conditions, our desired states are obtained as thesteady-state solution of the master equation of the system.     

Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features:A new approach

Recently,nonlinear displaced number states(NDNSs) have been manually introduced,in which the deformation function f(n) has been artificially added to the previously well-known displaced number states(DNSs).Indeed,just a simple comparison has been performed between the standard coherent state and nonlinear coherent state for the formation of NDNSs.In the present paper,after expressing enough physical motivation of our procedure,four distinct classes of NDNSs are presented by applying algebraic and group treatments.To achieve this purpose,by considering the DNSs and recalling the nonlinear coherent states formalism,the NDNSs are logically defined through an algebraic consideration.In addition,by using a particular class of Gilmore–Perelomov-type of SU(1,1) and a class of SU(2) coherent states,the NDNSs are introduced via group-theoretical approach.Then,in order to examine the nonclassical behavior of these states,sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed,in detail.     

Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

The SU（1,1） coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU（1,1） coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr Sommerfeld quantization rule yields the exact expression for the energy spectrum.     

Generation of SU（1,1） Intelligent States for the Motion of Two Trapped Ions

We propose a method for generating SU(1, 1) intelligent states for the center of mass and relative motional modes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the same as the direction of the two trapped ions‘ alignment. Under certain conditions, our desired states are obtained as the steady-state solution of the master equation of the system.     

Charmed baryon heavy-quark resonances with symmetry

We study charmed baryon resonances that are generated dynamically from a coupled-channel unitary approach that implements heavy-quark symmetry. Some states can already be identified with experimental observations, such as Ac（2595）, Ac（2660）, Ec（2902） or Ac（2941）, while others need a compilation of more experimental data as well as an extension of the model to include higher order contributions. We also compare our model to previous SU（4） schemes.     

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.     

Coupling Between the Group—Related Coherent States

When two representations of the Lie algebra are coupled,the coupling integral kernels are presented to relate the coupled to uncoupled group-related coherent states,These kernels have a connection with usual coupling coefficients.The explicit expressions of these kernels for SU(2),SO(4) and SUq(2) are given.When the direct product of three representations is formed in two ways,the recoupling integral kernels relating to the coupled group-related coherent states corresponding to two different schemes are introduced,and the relations between these kernels and the general recoupling coefficients are obtained.The properties of these kerels are discussed.     

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 state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.     

Squeezed Number State Solutions of Generalized Two-Mode Harmonic Oscillators Model:an Algebraic Approach

Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.     

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。     

Nonlinear squeezed states for SU(1,1) Lie algebra

The nonlinear extensions of the single-mode squeezed vacuum and squeezed coherent states are studied. We have constructed the nonlinear squeezed states (NLSS's) realization of SU(1,1) Lie algebra. Two cases of this realization are considered for unitary and non-unitary deformation operator function. The nonlinear squeezed coherent states (NLSCS's) are defined and special cases of these states are obtained. Some nonclassical properties of these states are discussed. The s-parameterized characteristic function and various moments are calculated. The Glauber second-order coherence function is calculated. The squeezing properties of the NLSCS's are studied. Analytical and numerical results for the quadrature component distributions for the NLSCS's are presented. A generation scheme for NLSCS's using the trapped ions centre-of-mass motion approach is proposed.     

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     

Representation mixing and the ideal description of mesons

Representation mixing of meson states is considered with particular reference to the 1 ←→ 15 mixing in SU(4). The 16 meson states are assigned to the representation (4*, 4) of a non-chiral group SU(4) ? SU(4), whose factors are related by charge-conjugation. Mass formula, mixing angles and electromagnetic mass shifts are rigorously derived. Connection of the present formalism with conventional quark model is pointed out and generalisations to higher groups SU(n) ? SU(n) as well as to higher representations, are indicated.     

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.

     

Coherent states associated with the groups SU(N) and SU(N, 1)

The coherent-state basis is constructed for symmetric representations of the groups SU(N) and SU(N, 1) and its properties are studied. The evolution of coherent states is considered. A relationship between the SU(N) coherent states and the Glauber coherent states is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–89, January, 1990.     

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。     

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。