Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Information

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

Roberto de J. León‐Montiel, H. M. Moya-Cessa

Published Jan 1, 2011• 18 citations
Publisher

Abstract

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.
DOI
10.1142/s0219749911007319

Related papers

Nonlinear coherent states for the Susskind-Glogower operators

León-Montiel, Roberto de Jesús, Moya-Cessa, Hector Manuel, Francisco Soto

We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with the Susskind-Glogower operators. We generalize the solution of the eigen- function problem to an arbitrary |mi initial condition. To analyze the obtained results, we plot the Husimi Q function, the photon number probability distribution and the Mandel Q-parameter. For both cases, we find that the constructed states exhibit interesting nonclassical features, such as amplitude squeezing and quantum interferences due to a self-splitting into two coherent-like states. Additionally, we show that non- linear coherent states may be modeled by propagating light in semi-infinite arrays of optical fibers.

arXiv:1303.2516•Mar 11, 2013•1 citation

Nonlinear coherent states for the Susskind-Glogower operators

Roberto de J. León‐Montiel, H. M. Moya-Cessa, Francisco Soto

Resumen en: We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also c...

Revista Mexicana de Física•Jan 1, 2011•7 citations

Nonlinear coherent states for the Susskind-Glogower operators

Roberto de J. León‐Montiel, H. M. Moya-Cessa, Francisco Soto

In this thesis, we construct nonlinear coherent states for the Susskind-Glogower\noperators by the application of the displacement operator on the vacuum state.\nWe also construct nonlinear coherent states as eigenfunctions of a Hamiltonian\nconstructed with the Susskind-Glogower operators. We generalize the solution\nto the eigenfunction problem to an arbitrary jmi initial condition. To analize\nthe obtained results, we plot the Husimi Q function, the photon number\nprobability distribution and the Mandel Q-parameter. For both cases, we nd\nthat the constructed states exhibit interesting nonclassical features such as\namplitude squeezing and quantum inteferences due to a self-splitting into two\ncoherent-like states. Additionally, we show that nonlinear coherent states may\nbe modelled by propagating light in semi-innite arrays of optical bers.

•May 1, 2010•2 citations

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

I. Ramos-Prieto, B. M. Rodríguez-Lara, H. M. Moya-Cessa

We propose a class of nonlinear coherent states which are experimentally feasible in cavity or ion-trap quantum electrodynamics. These quantum field states arise from a new type of photon addition and subtraction based on London phase operators, also known as Susskind–Glogower operators, that just displaces the mean photon number without scaling the photon distribution.

arXiv:1406.0749•International Journal of Quantum Information•Nov 1, 2014•15 citations

Generalized Susskind–Glogower coherent states

J.-P. Gazeau, Véronique Hussin, J. Moran +1 more

Susskind–Glogower coherent states, whose Fock expansion coefficients include Bessel functions, have recently attracted considerable attention for their optical properties. Nevertheless, identity resolution is still an open question, which is an essential mathematical property that defines an overcomplete basis in the Fock space and allows a coherent state quantization map. In this regard, the modified Susskind–Glogower coherent states have been introduced as an alternative family of states that resolve the identity resolution. In this paper, the quantization map related to the modified Susskind–Glogower coherent states is exploited, which naturally leads to a particular representation of the su(1,1) Lie algebra in its discrete series. The latter provides evidence about further generalizations of coherent states, built from the Susskind–Glogower ones by extending the indices of the Bessel functions of the first kind and, alternatively, by employing the modified Bessel functions of the second kind. In this form, the new families of Susskind–Glogower-I and Susskind–Glogower-II coherent states are introduced. The corresponding quantization maps are constructed so that they lead to general representations of elements of the su(1,1) and su(2) Lie algebras as generators of the SU(1, 1) and SU(2) unitary irreducible representations, respectively. For completeness, the optical properties related to the new families of coherent states are explored and compared with respect to some well-known optical states.

arXiv:2011.10303•Journal of Mathematical Physics•Jul 1, 2021•13 citations

New nonlinear coherent states based on hypergeometric-type operators

Alireza Dehghani, B. Mojaveri

The main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states. To do this, we first establish a class of hypergeometric type of generalized displacement operators, 1 F r ([0], [0, 1, ..., r − 1], za †), act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the Fock space which admit a resolution of the identity through a positive definite measure on the complex plane. Furthermore, realization of the compact form of these states, as functions of the position coordinate x for r = 2, leads to a generating function of the Hermite polynomials in terms of the modified Bessel function. Finally, studying some statistical characters reveals that they have indeed non-classical features such as squeezing, an anti-bunching effect and sub-Poissonian statistics, too.

Journal of Physics A Mathematical and Theoretical•Feb 20, 2012•18 citations
We construct nonlinear coherent states for the Susskind-Glogower operators by the application of the displacement operator on the vacuum state. We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian constructed with the Susskind-Glogower operators. We generalize the solution of the eigen- function problem to an arbitrary |mi initial condition. To analyze the obtained results, we plot the Husimi Q function, the photon number probability distribution and the Mandel Q-parameter. For both cases, we find that the constructed states exhibit interesting nonclassical features, such as amplitude squeezing and quantum interferences due to a self-splitting into two coherent-like states. Additionally, we show that non- linear coherent states may be modeled by propagating light in semi-infinite arrays of optical fibers.
In this thesis, we construct nonlinear coherent states for the Susskind-Glogower\noperators by the application of the displacement operator on the vacuum state.\nWe also construct nonlinear coherent states as eigenfunctions of a Hamiltonian\nconstructed with the Susskind-Glogower operators. We generalize the solution\nto the eigenfunction problem to an arbitrary jmi initial condition. To analize\nthe obtained results, we plot the Husimi Q function, the photon number\nprobability distribution and the Mandel Q-parameter. For both cases, we nd\nthat the constructed states exhibit interesting nonclassical features such as\namplitude squeezing and quantum inteferences due to a self-splitting into two\ncoherent-like states. Additionally, we show that nonlinear coherent states may\nbe modelled by propagating light in semi-innite arrays of optical bers.
Susskind–Glogower coherent states, whose Fock expansion coefficients include Bessel functions, have recently attracted considerable attention for their optical properties. Nevertheless, identity resolution is still an open question, which is an essential mathematical property that defines an overcomplete basis in the Fock space and allows a coherent state quantization map. In this regard, the modified Susskind–Glogower coherent states have been introduced as an alternative family of states that resolve the identity resolution. In this paper, the quantization map related to the modified Susskind–Glogower coherent states is exploited, which naturally leads to a particular representation of the su(1,1) Lie algebra in its discrete series. The latter provides evidence about further generalizations of coherent states, built from the Susskind–Glogower ones by extending the indices of the Bessel functions of the first kind and, alternatively, by employing the modified Bessel functions of the second kind. In this form, the new families of Susskind–Glogower-I and Susskind–Glogower-II coherent states are introduced. The corresponding quantization maps are constructed so that they lead to general representations of elements of the su(1,1) and su(2) Lie algebras as generators of the SU(1, 1) and SU(2) unitary irreducible representations, respectively. For completeness, the optical properties related to the new families of coherent states are explored and compared with respect to some well-known optical states.
The main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states. To do this, we first establish a class of hypergeometric type of generalized displacement operators, 1 F r ([0], [0, 1, ..., r − 1], za †), act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the Fock space which admit a resolution of the identity through a positive definite measure on the complex plane. Furthermore, realization of the compact form of these states, as functions of the position coordinate x for r = 2, leads to a generating function of the Hermite polynomials in terms of the modified Bessel function. Finally, studying some statistical characters reveals that they have indeed non-classical features such as squeezing, an anti-bunching effect and sub-Poissonian statistics, too.