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

The European Physical Journal D

Nonlinear squeezed states for SU(1,1) Lie algebra

A.‐S. F. Obada, G. M. Abd Al-Kader

Published Aug 31, 2006• 6 citations
Publisher
DOI
10.1140/epjd/e2006-00196-9

Related papers

Analytic Representations Based on SU(1,1) Lie Algebra Coherent States for Squeezed Displaced Fock States

G. M. Abd Al-Kader, A.‐S. F. Obada

Applied Categorical Structures•Nov 6, 2006•0 citations

Nonlinear Two-Mode Squeezed Vacuum States as Realization of SU(1,1) Lie Algebra

G. M. Abd Al-Kader, A.‐S. F. Obada

Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS’s) are constructed and special cases of these states are discussed. We have constructed the NTMSVS’s realization of SU(1,1) Lie algebra. Two cases of the definition are considered for unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed.

TURKISH JOURNAL OF PHYSICS•Jul 7, 2008•0 citations

Construction and Properties of Photon-Added su(1) Algebraic Squeezed States†

Hadiah Bint Monir, Shahid Iqbal

Journal of Russian Laser Research•Jan 1, 2020•5 citations

Nonlinear Two-Mode Squeezed Vacuum States as Realization of SU(1,1) Lie Algebra

OBADA, Gamal Mohamed ABD AL-KADER and Abdel-Sha

Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS's) are constructed and special cases of these states are discussed. We have constructed the NTMSVS's realization of SU(1,1) Lie algebra. Two cases of the definition are considered for unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed.

•Mar 1, 2008•0 citations

Interaction of squeezed states with nonlinear optical systems

Gerard J Milburn

•Jan 1, 1985•0 citations

SU(1,1) Nonlinear Coherent States

B. Mojaveri, Alireza Dehghani

The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group SU(1, 1). By using of a discrete, unitary and irreducible representation of the Lie algebra su(1, 1) wide range of generalized nonlinear coherent states(GNCS) have been introduced, which admit a resolution of the identity through positive definite measures on the complex plane. We have shown that realization of these states for different values of the deformation pa- rameters r = 1 and 2 lead to the well-known Klauder-Perelomov and Barut-Girardello coherent states associated to the Irreps of the Lie algebra su(1, 1), respectively. It is worth to mention that, like the canonical coherent states, GNCS possess the temporal stability property. Finally, studying some statistical characters implies that they have indeed nonclassical features such as squeezing, anti-bunching effect and sub-Poissonian statistics, too.

arXiv:1212.6888•Dec 31, 2012•0 citations
The idea of construction of the nonlinear coherent states based on the hypergeometric- type operators associated to the Weyl-Heisenberg group [J:P hys:A 45(2012) 095304], are generalized to the similar states for the arbitrary Lie group SU(1, 1). By using of a discrete, unitary and irreducible representation of the Lie algebra su(1, 1) wide range of generalized nonlinear coherent states(GNCS) have been introduced, which admit a resolution of the identity through positive definite measures on the complex plane. We have shown that realization of these states for different values of the deformation pa- rameters r = 1 and 2 lead to the well-known Klauder-Perelomov and Barut-Girardello coherent states associated to the Irreps of the Lie algebra su(1, 1), respectively. It is worth to mention that, like the canonical coherent states, GNCS possess the temporal stability property. Finally, studying some statistical characters implies that they have indeed nonclassical features such as squeezing, anti-bunching effect and sub-Poissonian statistics, too.