Gazeau–Klauder coherent states of the triangular-well potential

We develop generalized coherent states based on the Gazeau–Klauder formalism for the triangular well potential and discuss some of their properties. We study the Mandel parameter and the second-order correlation function for investigating the statistical properties. Moreover, we present the spatiotemporal evolution.     

Generalized Klauder–Perelomov and Gazeau–Klauder coherent states for Landau levels

Based on a pair of representations obtained for Lie algebra h₄, the Hilbert space corresponding to all quantum states of Landau levels is split into an infinite direct sum of infinite-dimensional Hilbert subspaces. For any one of the Hilbert subspaces, we get linear combinations of their bases as generalized coherent states—the so-called Klauder–Perelomov and Gazeau–Klauder.     

Gazeau–Klauder quasi-coherent states for the Morse oscillator

In the Letter, we have constructed and investigated some properties of the Gazeau–Klauder quasi-coherent states for the Morse potential, previously deduced by Roy and Roy. We have focused our attention on the thermal states and we have found the analytical form for the diagonal P-representation of the density operator.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Construction of the Barut–Girardello quasi coherent states for the Morse potential

The Morse oscillator (MO) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications in quantum mechanics to diatomic or polyatomic molecules, spectroscopy and so on. For this potential some kinds of coherent states (especially of the Klauder–Perelomov and Gazeau–Klauder kinds) have been constructed previously. In this paper we construct the coherent states of the Barut–Girardello kind (BG-CSs) for the MO potential, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi’s and P$P$-quasi distribution functions (for the mixed-thermal states) are also presented. Finally, we show that all obtained results for the BG-CSs of MO tend, in the harmonic limit, to the corresponding results for the coherent states of the one dimensional harmonic oscillator (CSs for the HO-1D).     

The nonclassical properties of the superposition involving two squeezing coherent states

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Superpositions of excited–deexcited coherent states and some of their non-classical properties

Applying the operator a + a⁺ to the superposed coherent states several times, superpositions of the excited–deexcited coherent states are obtained. Compared with the original superposed coherent states, these new states can have stronger squeezing and anti-bunching effects. The operation a + a⁺ can also induce squeezing or antibunching effect if the original states do not possess these properties. Calculations about the phase properties, the Q function and the Wigner function reflect the non-classical character of the excited–deexcited states from different aspects.     

Exclusive measurement of coherent η-photoproduction from the deuteron

Coherent photoproduction of η-mesons from the deuteron has been measured from threshold up to E _γ≈ 750 MeV using the photon spectrometer TAPS at the tagged photon facility at the Mainz microtron MAMI. For the first time, differential coherent cross-sections have been deduced from the coincident detection of the η-meson and the recoil deuteron. A missing-energy analysis was used for the suppression of background events so that a very clean identification of coherent η-photoproduction was achieved. The resulting cross-sections agree with previous experimental results except for angles around 90^° in the γd c.m. system where they are smaller. They are compared to various model calculations. Received: 5 April 2001 / Accepted: 3 September 2001     

Nonclassicality of photon-modulated spin coherent states in the Holstein—Primakoff realization

Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J_± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.     

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.     

Gazeau-Klauder type coherent states for hypergeometric type operators

Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.      

A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction

A theoretical scheme is presented for generating Gazeau-Klauder coherent states (GKCSs) via the generalization of degenerate Raman interaction with coupling constant to intensity dependent coupling. Firstly, we prove that in the intensity dependent degenerate Raman interaction, under particular conditions, the modified effective Hamiltonian can be used instead of Hamiltonian in the interaction picture, for describing the atom-field interaction. We suppose that the cavity field is initially prepared in a nonlinear CS, which is not temporally stable. As we will observe, after the occurrence of the interaction between atom and field, the generated state involves a superposition of GKCSs which are temporally stable and initial nonlinear CS. Under specific conditions which may be prepared, the generated state just includes GKCS. So, in this way we produced the GKCS, successfully.     

Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

Information cloning of harmonic oscillator coherent states

We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a measurement fidelity and calculate it for our case as well as for the Gaussian cloners.     

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.     

Superpositions of the dual family of nonlinear coherent states and their non-classical properties

Nonlinear coherent states (CSs) and their dual families were introduced recently. In this paper, we want to obtain their superposition and investigate their non-classical properties such as antibunching effect, quadrature squeezing and amplitude squared squeezing. For this purpose two types of superposition are considered. In the first type, we neglect the normalization factors of the two components of the dual pair, superpose them and then we normalize the obtained states, while in the second type we superpose the two normalized components and then again normalize the resultant states. As a physical realization, the formalism will then be applied to a special physical system with known nonlinearity function, i.e., Hydrogen-like spectrum. We continue with the (first type of) superposition of the dual pair of Gazeau-Klauder coherent states (GKCSs) as temporally stable CSs. An application of the proposal will be given by employing the Pöschl-Teller potential system. The numerical results are presented and discussed in detail, showing the effects of this special quantum interference.     

Amplitude-squared squeezing of superposition of coherent states

This paper discusses the amplitude-squared squeezing for the superposition of two coherent states with their phase differences being separately π/2, 3π/2, and π1, as well as for the superposition state of two pseudoclassical states. According to the analysis, it is found that the superposition state of two coherent states with their phase differences π/2 and 3π/2, and the superposition state of two pseudoclassical states both do exhibit the amplitude-squared squeezing. Also, some specific states are found to exhibit even stronger squeezing effects when relative phase of the superposition is equal to the average photon number. Amplitude-squared squeezing is dependent on the difference in phase between two coherent states.     

Nonlinear coherent states of the Fokas-Lagerstrom potential

In this paper, we introduce an algebraic approach to construct Fokas-Lagerstrom coherent states. To do so, we define deformed creation and annihilation operators associated to this system and investigate their algebra. We show that these operators satisfy the f-deformed Weyl-Heisenberg algebra. Then, we propose a theoretical scheme to generate the aforementioned coherent states. The present contribution shows that the Fokas-Lagerstrom nonlinear coherent states possess some non-classical features.     

多光子激发相干态的Wigner函数

Wigner函数的负性是非经典量子态的重要判据之一.利用Fock态表象下Wigner函数的一般表达式,重构了相干态｜z〉的k光子激发态｜+k,z〉～a^－k｜z〉（k≥1）的Wigner函数,并根据其数值结果讨论了该量子态的非经典特性（这里a^－1为Bose湮没算符的逆算符,其作用相当于Bose产生算符）.结果表明,不论k取奇数还是偶数,相干态的这些k光子激发态都具有非经典特性;而且k的取值越大,这些量子态的非经典特性越明显. 关键词： 非经典量子态 激发相干态 Wigner函数 非经典特性