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

Abstract

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. keyword: solvable quantum systems, nonlinear coherent states, entropic uncertainty relation, number-phase Wigner function PACS: 42.50.Dv, 03.65.-w

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

“…For example, the uncertainty for position and momentum reads as ΔxΔp ≥ 0.5. Following Shannon's ideas, one can supply an alternative mathematical formulation of the uncertainty principle by the inequality δxδp ≥ πe [39], where δx and δp are defined as the exponential of Shannon entropies associated with the probability distributions for x and p as follows [40,41]:…”

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

“…Let A and B be a pair of conjugate observables defined on an (s + 1)-dimensional space, each with complete set of eigenstates |a n and |b n respectively, satisfying the eigenvalue equations [10,16] A|a n = a n |a n , B|b n = b n |b n ,…”

“…Now, we have all requirements to introduce the number-phase entropic uncertainty relations for generalized coherent states associated to solvable quantum systems with degenerate discrete spectra. In the infinite s limit, the sum in (42) leads to following integral [10,20]…”

“…Then, in Section 4 the presented approach is applied to a particle confined in a two-dimensional box and three-dimensional harmonic oscillator, and next the nonclassicality of their associated coherent states is investigated, numerically. Finally in section 5, with the help of Gazeau-Klauder coherent states formalism [8], the dynamical evolution of the states will be introduced in section 2 are considered and based on this recognition [9,10], the time evolution of nonclassical features and number-phase entropic uncertainty relation for the considered degenerate physical systems are studied. arXiv:1101.2058v1 [quant-ph] 11 Jan 2011 2 Generalized coherent states for solvable quantum systems with degenerate spectra…”

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

“…Accordingly, one simply has f (n) = e n /n associated to solvable quantum systems. In this way the nonlinear CSs may be deduced corresponding to any solvable quantum system as [5]:…”