The minimum-uncertainty coherent states for Landau levels

Dehghani, A.; Fakhri, H.; Mojaveri, B.

doi:10.1063/1.4770258

Cited by 23 publications

(33 citation statements)

References 29 publications

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“…Here, m is an integer number and n is a nonnegative one together with n ≥ −m limitation. Each pair of operators (a, a † ) and (b, b † ) have the following explicit forms in terms of the polar coordinates 0 < r < ∞ and 0 ≤ ϕ < 2π for two-dimensional flat surface [53],…”

Section: Landau Levelsmentioning

confidence: 99%

“…These states were later applied successfully to some other models based on their Lie algebra symmetries by Glauber [2,3], Klauder [4,5], Sudarshan [6], Barut and Girardello [7] and Perelomov [8]. Additionally, for the models with one degree of freedom either discrete or was first studied by Malkin and Man'ko [40] and later by many others [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Landau Levelsmentioning

confidence: 99%

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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“…which are the Sturmian functions for the unitary irreducible representations of the su(1, 1) Lie algebra. Also, the Bargmann index k is k = m/2 + 1/2, and the other group number is just the radial quantum number n. Therefore we can construct the SU(1, 1) Perelomov number coherent states for this problem by substituting equation (44) into equation (24). By interchanging the order of summations and using the properties 48.7.6 and 48.7.8 of reference [29] we obtain ψ n,m = 2Γ(n + 1) Γ(n + m + 1)…”

Section: A Charged Particle In a Uniform Magnetic Field In The Symmetmentioning

confidence: 99%

“…However, different gauges give raise to the same electromagnetic field [18]. The coherent states for this problem have been obtained previously by using different formalisms, as can be seen in references [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 97%

An algebraic approach to a charged particle in a uniform magnetic field

et al. 2018

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We study the problem of a charged particle in a uniform magnetic field with two different gauges, known as Landau and symmetric gauges. By using a similarity transformation in terms of the displacement operator we show that, for the Landau gauge, the eigenfunctions for this problem are the harmonic oscillator number coherent states. In the symmetric gauge, we calculate the SU (1, 1) Perelomov number coherent states for this problem in cylindrical coordinates in a closed form. Finally, we show that these Perelomov number coherent states are related to the harmonic oscillator number coherent states by the contraction of the SU (1, 1) group to the Heisenberg-Weyl group.

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“…Using the constructed the minimum uncertainty two variable CSs,  , for a charged particle in the magnetic field as [28],…”

Section: Introducing Even and Odd Semi-css (Esemi-css And Osemi-css)mentioning

confidence: 99%

Nonclassical Properties of Even and Odd Semi-Coherent States

Salah¹

2017

IOSR JAP

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The minimum-uncertainty coherent states for Landau levels

Cited by 23 publications

References 29 publications

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

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

An algebraic approach to a charged particle in a uniform magnetic field

Nonclassical Properties of Even and Odd Semi-Coherent States

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