Showing papers on "Coherent states in mathematical physics published in 2010"
TL;DR: In this article, two classes of nonlinear coherent states were constructed using an exponential function of intensity of radiation field, where the nonlinearity function is defined as f(n) = exp(n)/p n, where p n is a tunable non-linearity parameter.
24 citations
TL;DR: In this article, a semi-classical state for Poschl-Teller potentials based on a supersymmetric quantum mechanics approach is presented, where the parameters of these "coherent" states are points in the classical phase space of these systems.
Abstract: We present a construction of semi-classical states for Poschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They minimize a special uncertainty relation. Like standard coherent states they resolve the identity with a uniform measure. They permit to establish the correspondence (quantization) between classical and quantum quantities. Finally, their time evolution is localized on the classical phase space trajectory.
22 citations
TL;DR: In this paper, the authors explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions, and study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas.
Abstract: This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.
16 citations
TL;DR: In this paper, the state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states, which are generated by the various Veronese embeddings of the underlying state space into higher-dimensional state spaces.
Abstract: The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of the underlying state space into higher-dimensional state spaces. This construction is applied to the parameterisation of generalised coherent states, which is useful for practical calculations and provides an elementary combinatorial approach to the geometry of the coherent state space. The results are extended to Hilbert spaces with indefinite inner products, leading to the introduction of a new kind of generalised coherent states.
16 citations
TL;DR: In this article, the authors investigated the geometry of the space of N-valent SU(2)-intertwiners and proposed a set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations.
Abstract: We investigate the geometry of the space of N-valent SU(2)-intertwiners. We propose a new set of holomorphic operators acting on this space and a new set of coherent states which are covariant under U(N) transformations. These states are labeled by elements of the Grassmannian Gr(N,2), they possess a direct geometrical interpretation in terms of framed polyhedra and are shown to be related to the well-known coherent intertwiners.
15 citations
TL;DR: In this paper, a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent state is presented, and the suQ(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established.
Abstract: In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The suQ(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su(1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.
14 citations
TL;DR: Carinena et al. as discussed by the authors constructed nonlinear coherent states or f-deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator.
Abstract: We construct nonlinear coherent states or f-deformed coherent states for a nonpolynomial nonlinear oscillator which can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (Carinena et al 2008 J. Phys. A: Math. Theor. 41 085301). The deformed annihilation and creation operators which are required to construct the nonlinear coherent states in the number basis are obtained from the solution of the Schrodinger equation. Using these operators, we construct generalized intelligent states, nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for this newly solvable system. We also report certain nonclassical properties exhibited by these nonlinear coherent states. In addition to the above, we consider the position-dependent mass Schrodinger equation associated with this solvable nonlinear oscillator and construct nonlinear coherent states, Gazeau–Klauder coherent states and the even and odd nonlinear coherent states for it. We also give explicit expressions of all these nonlinear coherent states by considering a mass profile which is often used for studying transport properties in semiconductors.
11 citations
TL;DR: In this article, two types of superposition of nonlinear coherent states (CSs) and their dual families were considered, in which the first type neglects the normalization factors of the two components of the dual pair, superpose them and then normalize the obtained states, while the second type superposes the two normalized components and then again normalizes the resultant states.
11 citations
TL;DR: In this article, a class of generalized coherent states with a new type of identity resolution is constructed by replacing the labeling parameter of the canonical coherent states by Meixner?Pollaczek polynomials with specific parameters.
Abstract: A class of generalized coherent states with a new type of the identity resolution is constructed by replacing the labeling parameter of the canonical coherent states by Meixner?Pollaczek polynomials with specific parameters. The constructed coherent states belong to the state Hilbert space of the Gol'dman?Krivchenkov Hamiltonian.
9 citations
Posted Content•
TL;DR: In this article, the authors reviewed the coherent states with particular application to the free particle system and emphasized the didactic advantages of the formalism, including the relation of coherent states to the Galilei group and with the Husimi distribution.
Abstract: The coherent states are reviewed with particular application to the free particle system. The didactic advantages of the formalism is emphasized. Several interesting features, like the relation of the coherent states with the Galilei group and with the Husimi distribution are presented. Keywords: quantum mechanics, coherent states, free particle.
7 citations
TL;DR: In this article, the authors obtained and investigated the regular eigenfunctions of simple differential operators xrdr + 1/dxr + 1, r = 1, 2,..., with the eigenvalues equal to 1.
Abstract: We obtain and investigate the regular eigenfunctions of simple differential operators xr dr + 1/dxr + 1, r = 1, 2, ..., with the eigenvalues equal to 1. With the help of these eigenfunctions, we construct a non-unitary analogue of a boson displacement operator which will be acting on the vacuum. In this way, we generate collective quantum states of the Fock space which are normalized and equipped with the resolution of unity with the positive weight functions that we obtain explicitly. These states are thus coherent states in the sense of Klauder. They span the truncated Fock space without first r lowest-lying basis states: |0, |1, ..., |r − 1. These states are squeezed, sub-Poissonian in nature and reminiscent of photon-added states in Agarwal and Tara (1991 Phys. Rev. A 43 492).
22 Dec 2010
TL;DR: In this paper, a unified approach to coherent atom optics, clinical magnetic resonance tomography and the bacterial protein dynamics of structural microbiology is presented, based on harmonic analysis on the three-dimensional Heisenberg Lie group.
Abstract: Due to photonic visualization, quantum physics is not restricted to the microworld. Starting off with synthetic aperture radar, the paper provides a unified approach to coherent atom optics, clinical magnetic resonance tomography and the bacterial protein dynamics of structural microbiology. Its mathematical base is harmonic analysis on the three‐dimensional Heisenberg Lie group with associated nilpotent Heisenberg algebra Lie(N).
TL;DR: Geometric positions of square roots of coherent states of CCR algebras are investigated in this paper along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will provide a new insight into quasi-equivalence problems of quasIFree states.
Abstract: Geometric positions of square roots of coherent states of CCR algebras are investigated along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will provide a new insight into quasi-equivalence problems of quasifree states.
Journal Article•
TL;DR: In this article, the authors assume that G = H ×τ K is the semidirect product of two locally compact groups H and K, respectively and consider the quasi regular representation on G.
Abstract: In this article, assume that G = H ×τ K is the semidirect product of two locally compact groups H and K , respectively and consider the quasi regular representation on G . Then for some closed subgroups of G we investigate an admissible condition to generate the Gilmore-Perelomov coherent states. The construction yields a wide variety of coherent states, labelled by a homogeneous space of G .
18 Jun 2010
TL;DR: In this article, the authors introduced a new definition of coherent states for quantum groups and showed that the use of such coherent states provided a complex description of homogeneous spaces of quantum groups.
Abstract: Noncommutative (super) spaces relating to the coherent states for quantum (super) groups are investigated. Introducing a new definition of coherent states, it is shown that for some examples the use of such coherent states provide a complex description of homogeneous spaces of quantum groups. We give a concise summary of our study on the cases of quantum harmonic oscillator group, SUq(2),SUq(1,1) and OSpq(1/2).
TL;DR: In this paper, the Laplace transform was used to derive the statistical and geometrical properties of nonlinear coherent states of the Barut-Girardello and Perelomov coherent states.
Abstract: Various aspects of coherent states of nonlinear $su(2)$ and $su(1,1)$ algebras are studied. It is shown that the nonlinear $su(1,1)$ Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.
03 Jan 2010
TL;DR: In this paper, a non-linear coherent state quantization of non-negative numbers and their associated nonlinear coherent states is proposed. But this procedure takes into account the circle topology of the classical motion.
Abstract: Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.