Photon-added nonlinear coherent states for a one-mode field in a Kerr medium

Abstract

We construct deformed photon-added nonlinear coherent states (DPANCSs) by application of the deformed creation operator upon the nonlinear coherent states obtained as eigenstates of the deformed annihilation operator and by application of a deformed displacement operator upon the vacuum state. We evaluate some statistical properties like the Mandel parameter, Husimi, and Wigner functions for these states and analyze their differences; we give closed analytical expressions for them. We found a profound difference in the statistical properties of the DPANCSs obtained from the two abovementioned generalizations.

Nonclassical properties of Hermite polynomial excitation on squeezed vacuum and its decoherence in phase-sensitive reservoirs

“…H can also be gotten by using Eqs. (14) and (16). In particular, when n = 0 (corresponding to the squeezed vacuum), the Mandel's Q parameter and the second-order correlation function are given by Q M = cosh 2r > 1, and g (2) = 3+1/ sinh 2 r > 3, respectively.…”

“…There are many schemes proposed to realize this purpose. Non-Gaussian operation, say photon addition and photon subtraction, has been widely employed to enhance the nonclassical properties of the input states [2][3][4][5][6][7][8][9][10][11][12][13][14]. For instance, a quantum-to-classical transition has been realized experimentally through single-photonadded coherent states of light [15].…”

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

“…These states originally introduced by Agarwal and Tara [24,25] have received much attention from quantum optics and information [26,27,28] for their statistical properties such as the photon-number distribution, the Mandel parameter, the squeezing parameter, the Wigner function etc. 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].…”

Engineering nonlinear coherent states as photon-added and photon-subtracted coherent states

“…These photon-added states can be approximately generated in the laboratory by conditional measurement in the Jaynes-Cummings dynamics [5], in a beam splitter [7,8], or in spontaneous parametric down-conversion [9][10][11][12], to mention a few examples. Additional proposals to realize them in cavity or ion-trap quantum electrodynamics (QED) [13], Kerr media [14], and in quantum mechanical systems with non-linear potentials [15] have also been produced. Single-photon added coherent states are known to be non-classical non-Gaussian states and, thus, useful for quantum information processing [12].…”