arXiv subjects

M. K. Tavassoly

Publications and source records attributed to M. K. Tavassoly.

33 records · Page 2Linked to original sources

arXiv2010

A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction

A theoretical scheme is presented for generating Gazeau-Klauder coherent states(GKCSs) via the generalization of degenerate Raman interaction with coupling constant to intensity-dependent coupling. Firstly, we prove that in the intensity-dependent degenerate Raman interaction, under particular conditions, the modified efective Hamiltonian can be used instead of Hamiltonian in the interaction picture, for describing the atom-field interaction. We suppose that the cavity field is initially prepared in a nonlinear CS, which is not temporally stable. As we will observe, after the occurrence of the interaction between atom and field, the generated state involves a superposition of GKCSs which are temporally stable and initial nonlinear CS. Under specific conditions which may be prepared, the generated state just includes GKCS. So, in this way we produced the GKCS, successfully.

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arXiv2010

On a general formalism of nonlinear charge coherent states, their quantum statistics and nonclassical properties

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 coher- ent 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 been also 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 non-degenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned cat- egories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statisti- cal 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.

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arXiv2010

Nonlinear Quantum Optical Spring

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of $ω$ to $ω\sqrt{1+μa^\dagger a}$ the mentioned idea can be established. In the present paper we generalize the approach of quantum optical spring (has been called by us as nonlinear quantum optical spring) with attention to the {\it dependence of frequency to the intensity of radiation field} that {\it naturally} observed in nonlinear coherent states. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters as particular quantum features will be revealed.

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arXiv2010

Superpositions of the dual family of nonlinear coherent states and their non-classical properties

Nonlinear coherent states (CSs) and their {\it dual families} were introduced recently. In this paper we want to obtain their superposition and investigate their non-classical properties such as antibunching effect, quadrature squeezing and amplitude squared squeezing. For this purpose two types of superposition are considered. In the first type we neglect the normalization factors of the two components of the dual pair, superpose them and then we normalize the obtained states, while in the second type we superpose the two normalized components and then again normalize the resultant states. As a physical realization, the formalism will then be applied to a special physical system with known nonlinearity function, i.e., Hydrogen-like spectrum. We continue with the (first type of) superposition of the dual pair of Gazeau-Klauder coherent states (GKCSs) as temporally stable CSs. An application of the proposal will be given by employing the Pöschl-Teller potential system. The numerical results are presented and discussed in detail, showing the effects of this special quantum interference.

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arXiv2009

Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra

In this letter, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time evolution of number-phase entropic uncertainty and Wigner function of the considered physical systems with the help of temporally stable Gazeau-Klauder coherent states.

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arXiv2009

Quantum statistical properties of some new classes of intelligent states associated with special quantum systems

Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems with a known discrete spectrum as well as the generalized coherent states with known nonlinearity function $f (n)$. As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with \textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'} and \textit{`hydrogen-like spectrum'} have been realized. Finally, the nonclassicality of the obtained states has been investigated. To achieve this purpose the quantum statistical properties using the Mandel parameter and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been established numerically.

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arXiv2009

Gazeau$-$Klauder squeezed states associated with solvable quantum systems

A formalism for the construction of some classes of Gazeau$-$Klauder squeezed states, corresponding to arbitrary solvable quantum systems with a known discrete spectrum, are introduced. As some physical applications, the proposed structure is applied to a few known quantum systems and then statistical properties as well as squeezing of the obtained squeezed states are studied. Finally, numerical results are presented.

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arXiv2009

New nonlinear coherent states associated to inverse bosonic and $f$-deformed ladder operators

Using the {\it nonlinear coherent states method}, a formalism for the construction of the coherent states associated to {\it "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.

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arXiv2009

Superposition of two nonlinear coherent states $\fracπ{2}$ out of phase and their nonclassical properties

Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\fracπ{2}$ out of phase. The formalism has then been applied to a few physical systems as "harmonious states", "SU(1,1) coherent states" and "the center of mass motion of trapped ion". Finally, the nonclassical properties such as sub-Poissonian statistics, quadrature squeezing, amplitude-squared squeezing and Wigner distribution function of the superposed states have been investigated, numerically. Especially, as we will observe the Wigner functions of the superposed states take negative values in phase space, while their original components do not.

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arXiv2009

Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach

In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be applied to few special solvable quantum systems with known discrete spectrum as well as to some new classes of nonlinear oscillators with particular nonlinearity functions. Finally the associated phase distributions and their nonclasscial properties such as the squeezing in number and phase operators have been investigated, numerically.

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arXiv2005

Unifying the Construction of Various Types of Generalized Coherent States

In this tutorial I intend to present some of the results I obtained through my PhD work in the "quantum optics group of the University of Isfahan" under consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and advisor, respectively. I will revisit some of the pioneering proposals recently developed the concept of generalized CSs. As it can be observed the customary three generalization methods {\it (symmetry, algebraic and dynamical)} have never been considered in neither of them. Our intention in this work is at first to investigate the lost ring between the customary three methods and the recently developed ones, as possible. For this purpose it has been devised general analytic descriptions, which successfully demonstrate how different varieties of CSs (which are nonlinear in nature) can be obtained by two processes, first the {\it "nonlinear CSs"} method and second by {\it "basis transformations on an underlying Hilbert spaces"}. As a result, I will systematize the recently introduced generalized CSs in a clear and concise way. It will be clear also, that how our results can be considered as a first step in the generation process of the mathematical physics CSs in the context of quantum optics. Besides this, some new results emerge from our studies. I introduce a large classes of generalized CSs, namely the {\it "dual family"} associated with each set of early known CSs. But, in this relation, the previous processes for constructing the dual pair of Gazeau-Klauder CSs fail to work well, so I outlined a rather different method based on the {\it "temporal stability"} requirement of generalized nonlinear CSs.

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arXiv2005

The Construction of the Dual Family of Gazeau-Klauder Coherent States via Temporally Stable Nonlinear Coherent States

Using the {\it analytic representation} of the so-called Gazeau-Klauder coherent states(CSs), we shall demonstrate that how a new class of generalized CSs namely the {\it family of dual states} associated with theses states can be constructed through viewing these states as {\it temporally stable nonlinear CSs}. Also we find that the ladder operators, as well as the displacement type operator corresponding to these two pairs of generalized CSs, may be easily obtained using our formalism, without employing the {\it supersymmetric quantum mechanics}(SUSYQM) techniques. Then, we have applied this method to some physical systems with known spectrum, such as Pöschl-Teller, infinite well, Morse potential and Hydrogen-like spectrum as some quantum mechanical systems. Finally, we propose the generalized form of Gazeau-Klauder CS and the corresponding dual family.

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arXiv2004

The Construction of Some Important Classes of Generalized Coherent states: The Nonlinear Coherent States Method

Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the {\it "nonlinear coherent states"} approach. As a result we obtained a {\it "unified method"} to construct a large class of coherent states which already have been introduced by different prescriptions.

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arXiv2004

Representations of Coherent and Squeezed States in a $f$-deformed Fock Space

We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_λ$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.

math-ph↗

arXiv2003

Representations of Coherent States in Non-orthogonal Bases

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair.

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