Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

Honarasa, Gholamreza; Tavassoly, M. K.; Hatami, Mohsen; Roknizadeh, R.

doi:10.1016/j.physa.2010.10.049

Cited by 15 publications

(8 citation statements)

References 22 publications

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“…These states may appear as stationary states of the center-of mass motion of a trapped ion [25,26]. NLCSs exhibit nonclassical features such as quadrature squeezing, sub-Poissonian statistics, anti-bunching, self-splitting effects and so on [27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

Mojaveri

Dehghani

2013

Eur. Phys. J. D

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In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1, 1) Lie algebra. This is why we call them the generalized su(1, 1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.

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Section: Introductionmentioning

confidence: 99%

Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

Mojaveri

Dehghani

2013

Eur. Phys. J. D

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“…These states may appear as stationary states of the center-of mass motion of a trapped ion [26,27]. NLCSs exhibit nonclassical features such as quadrature squeezing, sub-Poissonian statistics, anti-bunching, self-splitting effects and so on [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Generalized su(2) coherent states for the Landau levels and their nonclassical properties

Dehghani

Mojaveri

2013

Eur. Phys. J. D

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Following the lines of the recent papers [J. Phys. A: Math. Theor. 44, 495201 (2012); Eur. Phys. J. D 67, 179 (2013)], we construct here a new class of generalized coherent states related to the Landau levels, which can be used as the finite Fock subspaces for the representation of the su(2) Lie algebra. We establish the relationship between them and the deformed truncated coherent states. We have, also, shown that they satisfy the resolution of the identity property through a positive definite measures on the complex plane. Their nonclassical and quantum statistical properties such as quadrature squeezing, higher order 'su(2)' squeezing, anti-bunching and anti-correlation effects are studied in details. Particularly, the influence of the generalization on the nonclassical properties of two modes is clarified.continuous spectra-with no remark on the existence of a Lie algebra symmetry-Gazeau et al proposed new CSs, which were parametrized by two real parameters [9,10]. Moreover, there exist some considerations in connection with CSs corresponding to the shape invariance symmetries [11,12]. To construct CSs, four main different approaches the so-called Schrödinger, Klauder-Perelomov, Barut-Girardello, and Gazeau-Klauder methods have been found, so that the second and the third approaches rely directly on the Lie algebra symmetries and their corresponding generators. Here, it is necessary to emphasize that quantum coherence of states nowadays pervade many branches of physics such as quantum electrodynamics, solid-state physics, and nuclear and atomic physics, from both theoretical and experimental viewpoints.In addition to CSs, squeezed states (SSs) have attracted much attention during past decades. These are non-classical states of the electromagnetic field in which certain observables exhibit fluctuations less than the vacuum state [13]. These states are interesting because they can achieve lower quantum noise than the zero-point fluctuations of the vacuum or coherent states. Over the last four decades there have been several experimental demonstrations of nonclassical effects, such as the photon anti-bunching [14], sub-Poissonian statistics [15,16], and squeezing [17,18]. Also, considerable attention has been paid to the deformation of the harmonic oscillator algebra of creation and annihilation operators [19]. Some important physical concepts such as the CSs, the even-and odd-CSs for ordinary harmonic oscillator have been extended to deformation case. Moreover, there exist interesting quantum interference effects related to the quantum states that are namely superposition states, too [20,21]. Besides, superpositions of CSs can be prepared in the motion of a trapped ion [22,23]. With respect to the nonclassical effects, the coherent states turn out to define the limit between the classical and nonclassical behavior.Another type of generalization of CSs is the nonlinear coherent states (NLCSs), or f-CSs [24]. They are associated with nonlinear algebras and defined as the eigenstates of the annihilation operator ...

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“…In this subsection,by using the Hussin's methods for the degenerate energy spectrum [21,22], the coherent states of the free particle on the sphere are constructed.…”

Section: Gazeau-klauder Coherent Statesmentioning

confidence: 99%

Coherent States of Quantum Free Particle on the Spherical Space

et al. 2015

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In this paper, we study the quantum free particle on the spherical space by applying da costa approach for quantum particle on the curved space. We obtain the discrete energy eigenvalues and associated normalized eigenfunctions of the free particle on the sphere. In addition, we introduce the Gazeau-Klauder coherent states of free particle on the sphere. Then, the Gaussian coherent states is defined, which is used to describe the localized particle on the spherical space. Finally, we study the relation between the f -deformed coherent states and Gazeau-Klauder ones for this system.

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Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

Cited by 15 publications

References 22 publications

Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

Generalized su(2) coherent states for the Landau levels and their nonclassical properties

Coherent States of Quantum Free Particle on the Spherical Space

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