Coherent States with Complex Functions

The canonical coherent states are infinite series in powers of a complex number z. We present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions, and elementary functions. Further, we show that some of these classes do not furnish generalized oscillator algebras in the natural way. A reproducing kernel Hilbert space is discussed to each class of coherent states.     

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.

     

Generalized Photon Added and Subtracted f-Deformed Displaced Fock States

In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f-deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.     

Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties

We construct photon modulated coherent states of a generalized isotonic oscillator by expanding the newly introduced superposed operator through Weyl ordering method. We evaluate the parameter A ₃ and the s-parameterized quasi probability distribution function to confirm the non - classical nature of the states. We also calculate the identities related with the quadrature squeezing to explore the squeezing property of the states. Finally, we investigate the fidelity between the photon modulated coherent states and coherent states to quantify the non-Gaussianity of the states. The constructed states and their associated non - classical properties will add further knowledge on the potential.     

New Coherent States for the BDS-Hamiltonian

In the paper we construct a new set of coherent states for a deformed Hamiltonian of the harmonic oscillator, previously introduced by Beckers, Debergh, and Szafraniec, which we have called the BDS-Hamiltonian. This Hamiltonian depends on the new creation operator a ⁺, i.e. the usual creation operator displaced with the real quantity . In order to construct the coherent states, we use a new measure in the Hilbert space of the Hamiltonian eigenstates, in fact we change the inner product. This ansatz assures that the set of eigenstates be orthonormalized and complete. In the new inner product space the BDS-Hamiltonian is self-adjoint. Using these coherent states, we construct the corresponding density operator and we find the P-distribution function of the unnormalized density operator of the BDS-Hamiltonian. Also, we calculate some thermal averages related to the BDS-oscillators system which obey the quantum canonical distribution conditions.     

Coherent States of Two-Mode q-Oscillators with a q Root of Unity

When q is a root of unity, the coherent states of two-mode q-oscillators are constructed by introducing the generalized Grassmann variables.     

Entanglement in Bipartite Generalized Coherent States

Entanglement of formation in a class of bipartite generalized coherent states is discussed. It is shown that a positive parameter can be associated with these bipartite states so that the states with equal value for the parameter are of equal entanglement. For the class of states considered, the maximum possible entanglement of one ebit is attained if the value of the positive parameter is . It is shown that the entanglement of formation is one ebit when the relative phase between the composing states is π in the class of bipartite generalized coherent states considered.     

{Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc

The quantum algebras generated by the coherent states maps of the disc are investigated. It is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q-analysis. The applications of the analysis to star-product quantizations and q-special functions theory are given. Among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed, when the series is treated as a reproducing kernel. Received: 4 April 1996 / Accepted: 29 June 1997     

Generalized Two-Mode Squeezed States and Some Nonclassical Characteristics

A class of generalized two-mode squeezed states |φ〉 is presented, which are generated from the generalized two-mode squeezing operator U(γ,λ) acting on the two-mode coherent state |α ₁,α ₂〉. We first investigate some mathematical properties of U(γ,λ) including the squeezing transformation under U(γ,λ), ket-bra integral form in the coordinate representation, normally ordered form. Then we evaluate some nonclassical characteristics of the state |φ〉 such as higher-order squeezing behavior, entanglement analysis and analytical expression of the Wigner function.     

States as Morphisms

Using elementary categorical methods, we survey recent results concerning D-posets (equivalently effect algebras) of fuzzy sets and the corresponding category ID in which states are morphisms. First, we analyze the canonical structures carried by the unit interval I = [0,1] as the range of states and the impact of “states as morphisms” on the probability domains. Second, we analyze categories of various quantum and fuzzy structures and their relationships. Third, we describe some basic properties of ID and show that traditional probability domains such as fields of sets and bold algebras can be viewed as full subcategories of ID and probability measures on fields of sets and states on bold algebras become morphisms. Fourth, we discuss the categorical aspects of the transition from classical to fuzzy probability theory. We conclude with some remarks about generalized probability theory based on ID.     

Nonclassical properties and algebraic characteristics of negative binomial states in quantized radiation fields

We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Perelomov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they are excited geometric states. As intermediate states, they interpolate between the number states and geometric states. We also point out that they can be recognized as the nonlinear coherent states. Their nonclassical properties, such as sub-Poissonian distribution and squeezing effect are discussed. The quasiprobability distributions in phase space, namely the Q and Wigner functions, are studied in detail. We also propose two methods of generation of the negative binomial states. d 32.80.Pj Optical cooling of atoms; trapping Received 8 May 1999 and Received in final form 8 November 1999     

一类q变形广义相干叠加态的量子统计性质

研究了一类q变形广义相干态叠加态|ψ>=a|β>+be^iφ|βe^iδ>的量子统计性质，结果表明此种叠加态普遍存在压缩效应和光子反群聚效应.相干态间的位相差，叠加系数的位相差和广义相干态之间内积的幅值和位相的变化对迭加态的压缩效应和反群聚效应起着重要的作用. 关键词： q变形')" href="#">q变形 广义相干态 压缩效应 反群聚效应     

Photon-Added SU(1, 1) Coherent States and their Non-Classical Properties

The photon-added coherent states of Barut-Girardello and Perelomov types are constructed using Holstein-Primakoff realization of the su(1, 1) Lie algebra. Basic properties of the constructed states have been discussed. In addition, their non-classical features have been analyzed by computing photon detection probability distribution, Mandel Q-parameter and quadrature squeezing. It is shown that SU(1, 1) photon-added coherent states may exhibit sub-Poissonian statistics and quadrature squeezing for a chosen set of parameters. Moreover, it has been observed that their non-classical behavior increases as the number of added-photons increases.

     

Generalized Trio Coherent States

Generalized trio coherent states are made by superposing a number of trio coherent states. They possess inherent nonclassical properties such as sub-Poissonian distribution and violation of Cauchy-Schwarz inequalities. Their phase distribution in the framework of the Pegg and Barnett theory is discussed. We study the interaction of the radiation field prepared in a generalized trio coherent state with an atom in a superposition coherent state in the rotating wave approximation. We investigate the time dependence of the sub-Poissonian distribution and the violation of Cauchy-Schwarz inequalities for such a system. General conclusions reached are illustrated by numerical results.     

Even and Odd Nonlinear Negative Binomial States

In this paper the even and odd nonlinear negative binomial states of the radiation field are introduced. These states interpolates between even (odd) number states and the even (odd) nonlinear coherent states. The Glauber second-order correlation function is calculated for these states. The squeezing phenomenon (normal and amplitude-squared squeezing), the quasi-probability distribution function Q-function, Wigner-function and the phase properties, are also discussed. Examination of the resonance fluorescence against the present state is given. It has been shown that the atomic inversion is sensitive to any variation in the even and odd nonlinear negative binomial number M and the nonlinearity parameter η.     

Generation of Cluster-Type Entangled Coherent States via Cavity QED

In this paper, we present a scheme for generating cluster-type entangled coherent states via cavity QED. The scheme is based on the off-resonant interaction between one atom and N cavities, so the spontaneous emission of the atom can be ignored. The initial states of the N cavities are all prepared in vacuum states. We also discuss the experimental feasibility.     

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.     

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.     

New Even and Odd Nonlinear Coherent States and Their Nonclassical Properties

Based on Roy and Roy's work (Roy, B. and Roy, P. (2000). Journal of Optics B: Quantum Semiclass. Opt. 2, 65), a new type of even and odd nonlinear coherent states (NCSs) are defined. They result from Schrödinger cat states for deformed field. Using the numerical method, we study nonclassical properties of the new even and odd NCSs. It is shown that quantum statistical properties of the new even and odd NCSs are quite different from those of the usual even and odd coherent states (CSs). It is found that the squeezing only consists in the new even NCS, and the amplitude-squared squeezing and antibunching effect appear for both new even and odd NCSs in some ranges of ||.     

Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case

Multi-mode entangled coherent states are important resources for linear optics quantum computation and teleportation. Here we introduce the generalized balanced N-mode coherent states which recast in the multi-qudit case. The necessary and sufficient condition for bi-separability of such balanced N-mode coherent states is found. We particularly focus on pure and mixed multi-qubit and multi-qutrit like states and examine the degree of bipartite as well as tripartite entanglement using the concurrence measure. Unlike the N-qubit case, it is shown that there are qutrit states violating monogamy inequality. Using parity, displacement operator and beam splitters, we will propose a scheme for generating balanced N-mode entangled coherent states for even number of terms in superposition.