On theq-deformed coherent states of a generalizedf-oscillator

Abstract

Adopting the framework of the generalized q-deformed Heisenberg-Weyl algebra U (α,β,γ ) q (h 4 ), we present a mathematical procedure which leads us to obtain analytical expressions for a general class of q-deformed coherent states associated with the different patterns of the energy spectrum exhibited by the nonlinear f-oscillator. In particular, we establish the properties of a small group of q-deformed coherent states for α > γ > 0 with emphasis on the resolution of unity. As an application of these properties, we investigate the Robertson-Schrödinger uncertainty relation and the squeezing effect for the deformed coordinate and momentum operators, which are defined in terms of the abstract elements of this algebra. Furthermore, we also obtain the Wigner function and the correct quantum-mechanical marginal distributions in phase space.

Unified -deformation of oscillator algebra and two-dimensional conformal field theory

“…On the level of oscillator algebra, the study of multi-parameter deformations of the oscillator algebra was continued in the works [14,15,16,17,18].…”

“…Naturally, the increasing of the number of the deformation parameters makes the application of the deformed oscillator algebras more flexible in the practical applications. In the framework of one-parameter deformation this scheme combined with scheme of construction of the generalized deformed oscillator algebras [22] has given possibility to unify in unified framework [14,15,23,16,18] the well-known deformations of the oscillator algebra [6,4,5].…”

Entanglement generation with deformed Barut-Girardello coherent states as input states in an unitary beam splitter

“…They were introduced as a natural extension of the notion of coherent states [34,35]. Generalized deformation of Glauber states were constructed, see [36][37][38], as related to deformed harmonic oscillators. Deformed Peremolov and Barut-Girardello coherent states were also constructed as coherent states related to the quantum algebra U q (su(1, 1)) [39,40].…”

Algebraic properties of Rogers–Szegö functions: I. Applications in quantum optics

“…The second part of this paper is focussed basically on the construction process of coherent and phase states in accordance with the quantum-algebraic framework previously discussed. So, our first application has as reference guide the mathematical approach developed in [51] for an important class of coherent states, namely, those obtained from a determined eigenvalue equation for a given annihilation operator [23,24,25,26,27,28,29,30,31]. The eigenfunctions derived from this particular procedure are then expressed as an infinite expansion in terms of the RS functions whose coefficients satisfy a set of mathematical prerequesites that leads us to obtain, as a by-product, the excitation probability distribution for the q-deformed coherent state.…”

“…CX γ (z; q) = cos(γ)X γ (z; q) (It is important to mention that Nq ≡ B † B coincides with the standard number operator N only in the limit q → 1 −[29]. In this case, the operator N is subjected to the commutation relations [N, B] = −B and [N, B † ] = B † , which differ, by its turn, of those obtained in equation(30) for Nq.…”