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

Journal of Modern Optics

SU(1,1) Squeezing of SU(1,1) Generalized Coherent States

Vladimír Bužek

Published Mar 1, 1990• 157 citations
Publisher

Abstract

In this paper we have introduced a new class of the SU(1,1) coherent states which are the eigenstates of the generalized annihilation operator K_. We have also studied the SU(1,1) squeezing of the SU(1,1) generalized coherent states interacting with a nonlinear medium modelled as an anharmonic oscillator.
DOI
10.1080/09500349014550371

Related papers

Application of SU(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillator

Christopher C. Gerry

We consider the solvable model of nonabsorbing nonlinear medium modeled as an anharmonic oscillator interacting with squeezed light described as an SU(1,1) coherent state. We find that the squeezing is eventually revoked and furthermore that the greater the initial state is squeezed, the more rapidly the squeezing is revoked.

Physical Review A•Mar 1, 1987•114 citations

A new kind of nonlinear coherent states and their properties

Ji‐Suo Wang, Xiang‐Gao Meng, Bao‐Long Liang +1 more

A new kind of nonlinear coherent states, i.e. the k eigenstates of the powers B^k (k ≥ 3) of the generalized annihilation operator B^=a^†-1f(N^) of f-oscillators, are constructed using the inverse operators of the boson annihilation and creation operators. The set of these states may form a complete quantum mechanics representation. Using newly defined higher order squeezing and an antibunching, the properties of the Mth-order squeezing and the antibunching effect of the k states are investigated. The results show that the Mth-order [M = (n + 1/2)k; n = 0, 1, 2, …] squeezing effects exist in all of the k states when k is even and the antibunching effect exists in all of the k states.

Journal of Modern Optics•Jul 5, 2016•7 citations

Squeezing of the squared field amplitude by an anharmonic oscillator

Christopher C. Gerry, Edward R. Vrscay

Hillery [Opt. Commun. 62, 135 (1987)] has recently shown that the squeezing of the square of the field amplitude is a nonclassical effect. In this paper we show that the interaction of coherent light with a nonlinear medium modeled as a nonabsorbing anharmonic oscillator gives rise to this type of squeezing. We also show that this squeezing can be interpreted in terms of the Lie algebra of SU(1,1).

Physical Review A•Mar 1, 1988•40 citations

Quantum Statistical Properties of k-Quantum Nonlinear Coherent States

WANGJi-Suo, Ji-Suo, Liu . +5 more

In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powersBk (k ≥ 3) of the annihilation operator B=-a1/f(N) of f-oscillators, are introduced. In this paper, we introduce a newkind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied.The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when kis even. There is the antibunching effect in all of the k states.

理论物理通讯:英文版•Jan 1, 2004•0 citations

Generalized Coherent States Associated with the Cλ-Extended Oscillator

C. Quesne

Two new types of coherent states associated with the Cλ-extended oscillator, where Cλ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the Cλ-extended oscillator spectrum generating algebra for higher λ values. The second ones, which are eigenstates of the Cλ-extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the Cλ-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the Cλ-extended oscillator algebra are realized as differential-operatorvalued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited. 1 1

•Jan 1, 2001•18 citations

Quantum Statistical Properties of κ-Quantum Nonlinear Coherent States

Ji‐Suo Wang, Tang-Kun Liu, Feng Jian +1 more

In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers (B) over cap (k) (k greater than or equal to 3) of the annihilation operator (B) over cap = (a) over cap1/f((N) over cap) of f-oscillators, are introduced. In this paper, we introduce a new kind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied. The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when k is even. There is the antibunching effect in all of the k states.

Communications in Theoretical Physics•Sep 15, 2004•1 citation
A new kind of nonlinear coherent states, i.e. the k eigenstates of the powers B^k (k ≥ 3) of the generalized annihilation operator B^=a^†-1f(N^) of f-oscillators, are constructed using the inverse operators of the boson annihilation and creation operators. The set of these states may form a complete quantum mechanics representation. Using newly defined higher order squeezing and an antibunching, the properties of the Mth-order squeezing and the antibunching effect of the k states are investigated. The results show that the Mth-order [M = (n + 1/2)k; n = 0, 1, 2, …] squeezing effects exist in all of the k states when k is even and the antibunching effect exists in all of the k states.
In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powersBk (k ≥ 3) of the annihilation operator B=-a1/f(N) of f-oscillators, are introduced. In this paper, we introduce a newkind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied.The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when kis even. There is the antibunching effect in all of the k states.
Two new types of coherent states associated with the Cλ-extended oscillator, where Cλ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the Cλ-extended oscillator spectrum generating algebra for higher λ values. The second ones, which are eigenstates of the Cλ-extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the Cλ-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the Cλ-extended oscillator algebra are realized as differential-operatorvalued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited. 1 1
In our preceding work, a class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers (B) over cap (k) (k greater than or equal to 3) of the annihilation operator (B) over cap = (a) over cap1/f((N) over cap) of f-oscillators, are introduced. In this paper, we introduce a new kind of higher-order squeezing and an antibunching effect. The quantum statistical properties of the k states are studied. The result shows that the M-th order [M = (n + 1/2)k; n = 0, 1,...] squeezing effects exist in all of the k states when k is even. There is the antibunching effect in all of the k states.