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 Mathematical Physics

Two new types of quantum states generated via higher powers of Bogoliubov’s transformation

Wei Wu, Ling-An Wu

Published Apr 16, 2004• 5 citations
Publisher

Abstract

By applying higher powers of Bogoliubov’s transformation operator b†=ν*a+μ*a† to the even and odd coherent states we construct mathematically two new types of quantum states. Various special functions and mathematical formulations are used to obtain the matrix elements for the states in the coherent state representation. The nonclassical nature of these states is found to be related to their quantum coherence in phase space. The interference effects can also be regarded as a consequence of the oscillatory behavior of the special functions in the structure of the states.

DOI
10.1063/1.1688434

Related papers

A new class of quantum states generated by m -fold application of Bogoliubov's transformation

Wei Wu, Ling-An Wu, Xin Zong-Zheng

By applying higher powers of the Bogoliubov transformation operator bdagger = v*a + mu*adagger to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters lambda and rho, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.

Chinese Physics•Jul 29, 2004•1 citation

Quantum statistical properties of the generalized excited even and odd coherent states

Wei Wu, Ling-An Wu

We construct mathematically two new types of quantum state which we call the generalized excited even and odd coherent states of the radiation field. They are created by repeatedly applying the pseudo-creation operator b † = ν ∗ a + μ ∗ a † to the even and odd coherent states m times, respectively. Analytic expressions for the quantum statistical properties are derived, and through numerical computation it is found that these states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. These states may have interesting significance if they can be realized experimentally.

Journal of Optics B Quantum and Semiclassical Optics•Jul 23, 2003•7 citations

Quantum Properties of Two-Mode Squeezed Even and Odd Coherent States

Jing Zhang, Wei Wu, Meng Shao-ying

Two new types of quantum states are constructed by applying the operator s (ξ) = exp (ξ* ab −ξ a † b † ) on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy–Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.

Communications in Theoretical Physics•Feb 1, 2007•4 citations

Studies on nonlinear coherent states

S. Sivakumar

Nonclassical states of light are of fundamental importance in quantum optics. The properties of these states are due to the quantal nature of the electromagnetic field. In recent years there have been many experimental demonstrations of the realizability of nonclassical states in various physical schemes such as resonance fluorescence, four-wave mixing, centre-of-mass motion of a trapped ion and manipulation of field in a cavity. It is of interest to introduce new classes of nonclassical states and investigate their properties. In this context, generalization of the concept of coherent states (CSs) has played a major role. New concepts such as the nonlinear coherent states (NCSs) and interference in phase space have emerged from such studies. In this tutorial review we are concerned with the construction of new classes of nonclassical states by generalizing the notion of CSs. Our investigations on the photon-added coherent states (PACSs) indicate that these states can be interpreted as NCSs. Also, we introduce a new class of nonclassical states related to the PACSs. Having introduced a realizable example of NCSs, we extend the notion of even and odd CSs to the case of NCSs by introducing even and odd NCSs. With this new definition we interrelate some of the well known states of light. We suggest a scheme to generate a class of even and odd NCSs in the centre-of-mass motion of a trapped, laser-cooled, two-level ion.

Journal of Optics B Quantum and Semiclassical Optics•Nov 21, 2000•109 citations

A new class off-deformed charge coherent states and their nonclassical properties

M Mortazavi, M K Tavassoly

Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f -deformed ladder operators and construct a new class of f -deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

arXiv:1204.2673•Journal of Physics A Mathematical and Theoretical•May 30, 2012•7 citations

Some nonclassical properties of a finite dimensional even and odd pair coherent state

Meng Xiang-Guo, Ji‐Suo Wang, 聊城大学物理系,聊城 252059

The exponential form of even and odd pair coherent state (EOPCS) is constructed. The EOPCS is generalized to a finite dimensional EOPCS in the Hilbert space, and then its orthonormalized property, completeness relations and some noncalssical properties are discussed. It is shown that the finite dimensional EOPCS has normalized and completeness relations, but not orthogonal relations. By virtue of the numerical computation method, we find that, for any value of q, in different ranges of the parameter |ξ| the 5-dimensional EOPCS for the modes 1 and 2 exhibit anti-bunching effect and the photons between the two modes are always correlated. The different peak structures of the phase probability distributions for the 7-dimensional EOPCS show remarkably different quantum interference properties.

Acta Physica Sinica•Jan 1, 2007•7 citations
By applying higher powers of Bogoliubov’s transformation operator b†=νa+μa† to the even and odd coherent states we construct mathematically two new types of quantum states. Various special functions and mathematical formulations are used to obtain the matrix elements for the states in the coherent state representation. The nonclassical nature of these states is found to be related to their quantum coherence in phase space. The interference effects can also be regarded as a consequence of the oscillatory behavior of the special functions in the structure of the states.
By applying higher powers of the Bogoliubov transformation operator bdagger = v*a + mu*adagger to the two-photon coherent states (or minimum uncertainty squeezed states) we construct a new type of quantum state which we call the generalized excited two-photon coherent states. Analytic expressions for the quantum statistical properties are derived, and through numerical computation the phase space quasi-probability distributions are found. These states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. For particular values of two parameters lambda and rho, these generalized states reduce to other classes of coherent states formerly reported. Our theory thus presents a much broader approach to these types of quantum states.
We construct mathematically two new types of quantum state which we call the generalized excited even and odd coherent states of the radiation field. They are created by repeatedly applying the pseudo-creation operator b † = ν ∗ a + μ ∗ a † to the even and odd coherent states m times, respectively. Analytic expressions for the quantum statistical properties are derived, and through numerical computation it is found that these states can exhibit highly nonclassical behaviour depending on the degree of excitation m and other parameters. These states may have interesting significance if they can be realized experimentally.
Nonclassical states of light are of fundamental importance in quantum optics. The properties of these states are due to the quantal nature of the electromagnetic field. In recent years there have been many experimental demonstrations of the realizability of nonclassical states in various physical schemes such as resonance fluorescence, four-wave mixing, centre-of-mass motion of a trapped ion and manipulation of field in a cavity. It is of interest to introduce new classes of nonclassical states and investigate their properties. In this context, generalization of the concept of coherent states (CSs) has played a major role. New concepts such as the nonlinear coherent states (NCSs) and interference in phase space have emerged from such studies. In this tutorial review we are concerned with the construction of new classes of nonclassical states by generalizing the notion of CSs. Our investigations on the photon-added coherent states (PACSs) indicate that these states can be interpreted as NCSs. Also, we introduce a new class of nonclassical states related to the PACSs. Having introduced a realizable example of NCSs, we extend the notion of even and odd CSs to the case of NCSs by introducing even and odd NCSs. With this new definition we interrelate some of the well known states of light. We suggest a scheme to generate a class of even and odd NCSs in the centre-of-mass motion of a trapped, laser-cooled, two-level ion.
Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f -deformed ladder operators and construct a new class of f -deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
The exponential form of even and odd pair coherent state (EOPCS) is constructed. The EOPCS is generalized to a finite dimensional EOPCS in the Hilbert space, and then its orthonormalized property, completeness relations and some noncalssical properties are discussed. It is shown that the finite dimensional EOPCS has normalized and completeness relations, but not orthogonal relations. By virtue of the numerical computation method, we find that, for any value of q, in different ranges of the parameter |ξ| the 5-dimensional EOPCS for the modes 1 and 2 exhibit anti-bunching effect and the photons between the two modes are always correlated. The different peak structures of the phase probability distributions for the 7-dimensional EOPCS show remarkably different quantum interference properties.