Generalized photon-added associated hypergeometric coherent states: characterization and relevant properties

Abstract

This paper presents the construction of a new set of generalized photonadded coherent states related to associated hypergeometric functions introduced in our previous work (Hounkonnou M N and Sodoga K 2005 J. Phys. A: Math. Gen 38 7851). These states satisfy all required mathematical and physical properties. The associated Stieltjes power-moment problem is explicitly solved by using Meijer's G-function and the Mellin inversion theorem. Relevant quantum optical and thermal characteristics are investigated. The formalism is applied to particular cases of the associated Hermite, Laguerre, Jacobi polynomials and hypergeometric functions. Their corresponding states exhibit sub-Poissonian photon number statistics.

Mehler-Heine asymptotics and zeros of some Meijer G-functions

“…Other recent studies on Meijer G-functions include [6][7][8]. In addition, the Meijer G-functions have been applied in various branches of physics, including quantum mechanics (e.g., in the field of coherent states [9][10][11]), physical models [12], nuclear physics [13,14] and thermonuclear reactions [15].…”

“…In fact, we will obtain a limit relation between the scaled zeros of the function (10) and the zeros of the limit function in expression (11). With that purpose, we shall recall the properties of the Bessel function of the first kind and study the distribution of the zeros of  = a a a -J z z J z ( ) ( ) depending on the value of a Î -  ⧹ .…”

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

“…We show that these states satisfy the Klauder's mathematical requirement to build coherent states. We also explore the statistical properties [29][30][31][32][33][34][35][36] of these states, such as the photon distribution, the photon mean number, the intensity correlation and the Mandel parameter. We find that these states are sub-Poissonian in nature.…”

Photon-added BarutGirardello like coherent states of time-dependent Landau problem

“…Various generalizations of these states taking into account their statistical properties were also performed [29,30,31,32]. Recently, one of us addressed conjonctly the study of photon added states into the generalized associated hypergeometric coherent states [33] and into a full characterization of shape invariant potentials using algebraic approach based on the supersymmetric quantum mechanics [34]. The original construction of photon added coherent states (PACSs) [24,25] obtained from the conventionnal coherent states based on the Weyl-Heisenberg group has been extended to a number of Lie groups with square integrable representations.…”