Showing papers on "Coherent states in mathematical physics published in 2008"
TL;DR: In this article, the eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schrodinger equation, and various reductions of the symmetry algebra of the Askey-Wilson system are explored in detail.
Abstract: Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schr\"odinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.
45 citations
TL;DR: In this paper, the authors construct nonlinear coherent states by the application of a deformed displacement operator acting upon the vacuum state and as approximate eigenstates of the deformed annihilation operator.
Abstract: We construct nonlinear coherent states by the application of a deformed displacement operator acting upon the vacuum state and as approximate eigenstates of a deformed annihilation operator. These states are used to evaluate the temporal evolution of the average value of the momentum and the diplacement coordinate as well as their dispersions. We also construct even and odd combinations of these nonlinear coherent states and compute their second order correlation function in order to analyze their statistical behavior.
43 citations
TL;DR: In this paper, the authors demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of reproducing kernel Hilbert space, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions.
Abstract: We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions. It turns out that nonlinear coherent states, of the type widely studied in quantum optics, are a particularly useful class of coherent states from this point of view, in that they contain many of the standard statistical distributions. We also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions.
33 citations
TL;DR: In this article, a formalism for the construction of coherent states associated with inverse bosonic operators and their dual family has been proposed using nonlinear coherent states method and applied to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states.
Abstract: Using the nonlinear coherent states method, a formalism for the construction of the coherent states associated with 'inverse bosonic operators' and their dual family has been proposed. Generalizing the approach, the 'inverse of f-deformed ladder operators' corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Finally, after applying the proposal to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been investigated.
22 citations
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TL;DR: In this paper, the formation of topological defects in quantum field theory and the relation between fractals and coherent states are discussed, and the functional realization of fractals in terms of the q-deformed algebra of coherent states is also presented.
Abstract: In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical structure of quantum field theory with particular reference to the processes of non-equilibrium symmetry breaking. The functional realization of fractals in terms of the q-deformed algebra of coherent states is also presented. From one side, this sheds some light on the dynamical formation of fractals. From the other side, it also exhibits the fractal nature of coherent states, thus opening new perspectives in the analysis of those phenomena where coherent states play a relevant role. The global nature of fractals appears to emerge from local deformation processes and fractal properties are incorporated in the framework of the theory of entire analytical functions.
18 citations
TL;DR: In this article, the authors present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states (psi_1) and psi_2) for the case of coherent states.
Abstract: We present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states (psi_1)^k and (psi_2)^l. We consider two cases: 1) The two unknown states psi_1 and psi_2 are arbitrary states of qudits. 2) Alternatively, they are coherent states of a harmonic oscillator. For the case of coherent states we propose a simple experimental realization of the optimal "comparison" machine composed of a finite number of beam-splitters and a single photodetector.
17 citations
TL;DR: In this article, the fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed, and the authors propose and demonstrate the superior cloning of coherent states under the Gaussian assumption.
Abstract: The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and feedforward.
16 citations
TL;DR: In this paper, the Gazeau-Klauder coherent states for the trigonometric Rosen-Morse potential were constructed and the resolution of unity, temporal stability, and action identity conditions were satisfied.
Abstract: The Gazeau–Klauder coherent states for the trigonometric Rosen–Morse potential are constructed. It is shown that the resolution of unity, temporal stability, and action identity conditions are satisfied for the coherent states. The Mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states.
14 citations
TL;DR: In this paper, the coherent states for a particle in the noncentral Hartmann potential were obtained by transforming the problem into four isotropic oscillators evolving in a parametric time.
Abstract: We obtain the coherent states for a particle in the noncentral Hartmann potential by transforming the problem into four isotropic oscillators evolving in a parametric time. We use path integration over the holomorphic coordinates to find the quantum states for these oscillators. The decomposition of the transition amplitudes gives the coherent states and their parametric-time evolution for the particle in the Hartmann potential. We also derive the coherent states in the parabolic coordinates by considering the transition amplitudes between the coherent states and eigenstates in the configuration space.
10 citations
TL;DR: In this article, a new family of vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented, which allow a consistent quantization of the classical phase space and observables for a particle in this potential.
9 citations
TL;DR: In this article, discrete coherent states for a system of qubits were introduced in terms of eigenstates of the finite Fourier transform and the properties of these states were pictured in phase space by resorting to the discrete Wigner function.
Abstract: Discrete coherent states for a system of $n$ qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function
TL;DR: In this paper, the coherent states for a system of time-dependent singular potentials coupled to inverted CK (Caldirola-Kanai) oscillator are investigated by employing invariant operator method and Lie algebraic approach.
TL;DR: In this article, the Fock space representations of classical quantum affine algebras using combinatorics of Young walls are constructed, and the crystal graphs of these representations can be realized as the abstract crystal consisting of proper Young walls.
Abstract: We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the abstract crystal consisting of proper Young walls. Finally, we give a generalized version of Lascoux-Leclerc-Thibon algorithm for computing the global bases of the basic representations of classical quantum affine algebras.
TL;DR: In this paper, it was shown that the qubit can be expressed through coherent states, i.e., a message is expressed as a tensor product of coherent states and the information can be transmitted by using a classical channel.
Abstract: In this paper we have showed that the qubit can be expressed through the coherent states. Consequently, a message, i.e. a sequence of qubits, is expressed as a tensor product of coherent states. In the quantum information theory and practice, only the code and key message are expressed as a sequence of qubits, i.e. through a quantum channel, the properly information will be transmitted by using a classical channel. Even if the most used coherent states in the quantum information theory are the coherent states of the harmonic oscillator (particularly, expressing by them the Schrodinger “cat states” and the Bell states), several authors have been demonstrated that other kind of coherent states may be used in quantum information theory. For the ensembles of qubits, we must use the density operator, in order to describe the informational content of the ensemble. The diagonal representation of the density operator, in the coherent state representation, is also useful to examine the entanglement of the states.
TL;DR: In this article, the eigenvalue problem satisfied by intelligent states (IS) is solved, and some realizations for the results of IS are constructed and some applications are discussed.
Abstract: Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.
TL;DR: In this paper, the entanglement of superpositions of coherent states via a harmonic oscillator Hamiltonian was analyzed, which is quadratic in the interaction between the particles and symmetric with respect to particle exchange.
Abstract: In this paper we analyze the entanglement of superpositions of coherent states via a harmonic oscillator Hamiltonian that is quadratic in the interaction between the particles and symmetric with respect to particle exchange. Quantum superpositions of coherent states are commonly referred to as “Schrodinger cat states” 1. When the coherent states are only weakly excited, n
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07 Jul 2008
TL;DR: In this paper, a perturbation expansion of the inverse of the volume operator was constructed for spin networks with planar symmetry, and the authors proved that these SC states form a complete subset of the overcomplete set of coherent states.
Abstract: This paper is the second of two which construct coherent states for spin networks with planar symmetry. Paper 1 constructs set of coherent states peaked at specific values of holonomy and triad. These operators acting on the coherent state give back the coherent state plus small correction (SC) states. The present paper proves that these SC states form a complete subset of the overcomplete set of coherent states. The subset is used to construct a perturbation expansion of the inverse of the volume operator. Appendices calculate the standard deviations of the angles occurring in the holonomies, demonstrate that standard deviations are given by matrix elements of the SC states, and estimate the rate of spreading of a coherent state wave packet.
Journal Article•
TL;DR: In this article, a nonlinear extension of the two-mode squeezed vacuum states (NTMSVS) is constructed and special cases of these states are discussed for unitary and non-unitary deformation operator functions.
Abstract: Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS’s) are constructed and special cases of these states are discussed. We have constructed the NTMSVS’s realization of SU(1,1) Lie algebra. Two cases of the definition are considered for unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed.
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TL;DR: In this article, a representation of the Cuntz algebra in the space of (complex valued) functions on p-adic disk is introduced and the relation of this representation and the free coherent states is investigated.
Abstract: Representation of the Cuntz algebra in the space of (complex valued) functions on p–adic disk is introduced The relation of this representation and the free coherent states isinvestigated 1 Introduction The present paper combines the investigations on p–adic mathematical physics and noncommu-tative probability We introduce the representation of the Cuntz algebra in the space of (complexvalued) functions on p–adic disk and investigate the relation of this representation and the freecoherent states The representation which we introduce will be unitarily equivalent to one of therepresentation considered by Bratteli and Yorgensen in [1] (without use of p–adic analysis)Continuing the investigations of [2], [3], [4], we investigate the free coherent states (or shortlyFCS), which are (unbounded) eigenvectors of the linear combination of annihilators in the freeFock space In [2], [3] it was shown that the space of the free coherent states is highly degeneratefor the fixed eigenvalue λ (and infinite dimensional), and this degeneracy is naturally described bythe space D
01 Aug 2008
TL;DR: In this article, a new class of Bogoliubov transformations is introduced, which generalize the notion of squeezed states, and the transformation of the ordinary annihilation and creation operators under this unitary transformation leads to the introduction of multi-photon coherent states.
Abstract: Using Lie algebra methods, we find a new class of Bogoliubov transformations which generalize the notion of squeezed states. The Hamiltonians for the simple harmonic and anharmonic oscillators, turn out to be the generators of a Lie group, whose other generators may be found exactly, or up to any desired order of the perturbation parameter. An element of this Lie group, which is realized as the multi-photon operator, transforms the anharmonic Hamiltonian to the harmonic one. The transformation of the ordinary annihilation and creation operators under this unitary transformation leads to the introduction of multi-photon coherent states. We specifically consider four-photon coherent states in detail and study the time dependent position and momentum uncertainties in these states.
TL;DR: In this article, the Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon's coherent states (even and odd coherent states), are studied.
Abstract: The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.
13 Jul 2008
TL;DR: In this paper, a general linear optics based approach to implement contractive transformations that map products of N coherent states to products of M coherent states (M≤N) and apply it to nondestructive quantum database search is presented.
Abstract: We present a general linear optics based approach to implement contractive transformations that map products of N coherent states to products of M coherent states (M≤N) and apply it to nondestructive quantum database search.
TL;DR: The coherent states of the SU(1,1) group can be divided into two broad categories: (a) the Barut-Girardello coherent states (BGCSs) and (b) the Perelomov coherentStates (PCSs).
Abstract: The coherent states (CSs) of the SU(1,1) group can be divided into two broad categories: (a) the Barut-Girardello coherent states (BGCSs) and (b) the Perelomov coherent states (PCSs). Some definitions for the squeezed displaced Fock states (SDFSs) are given. The hyperbolic analytic representation in the complex plane is considered. An analytic representation of the SU(1,1) Lie group is given and the representation in the unit disk based on the SU(1,1) PCSs for SDFSs is considered.
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TL;DR: In this article, the authors studied the interaction between several fields initially in coherent states and gave a completely algebraic solution to explain why coherent states remain coherent states when subject to non-Markovian dissipation.
Abstract: We study the interaction between several fields initially in coherent states. The solution allows us to explain why coherent states remain coherent states when subject to non-Markovian dissipation. We first study the interaction between two fields and show that this is the building block of the total interaction. We give a completely algebraic solution of this system.
01 Jan 2008
TL;DR: In this paper, a unified approach for finding coherent states of polynomially deformed algebras such as the quadratic and Higgs algeses is presented.
Abstract: We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used , for the non compact cases, to obtain the annihilation operator coherent states, by finding the canonical conjugates of these operators. Generalized coherent states, in the Perelomov sense also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems.
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TL;DR: In this article, a perturbation expansion of the inverse of the volume operator was constructed for spin networks with planar symmetry, and the authors proved that these SC states form a complete subset of the overcomplete set of coherent states.
Abstract: This paper is the second of two which construct coherent states for spin networks with planar symmetry. Paper 1 constructs set of coherent states peaked at specific values of holonomy and triad. These operators acting on the coherent state give back the coherent state plus small correction (SC) states. The present paper proves that these SC states form a complete subset of the overcomplete set of coherent states. The subset is used to construct a perturbation expansion of the inverse of the volume operator. Appendices calculate the standard deviations of the angles occurring in the holonomies, demonstrate that standard deviations are given by matrix elements of the SC states, and estimate the rate of spreading of a coherent state wave packet.
TL;DR: In this paper, a new model of the quantum oscillator, related to the discrete q-Hermite polynomials of the second type, is presented, where position and momentum operators in the model are appropriate operators of the Fock representation of a deformation of the Heisenberg algebra.
Abstract: We construct a new model of the quantum oscillator, which is related to the discrete q-Hermite polynomials of the second type. The position and momentum operators in the model are appropriate operators of the Fock representation of a deformation of the Heisenberg algebra. These operators have a discrete non-degenerate spectra. These spectra are spread over the whole real line. Coordinate and momentum realizations of the model are constructed. Coherent states are explicitly given.