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

Acta Physica Sinica

MATHEMATICAL STRUCTURE OF THE EIGENSTATES OF OPERATOR ak AND THEIR PROPERTIES

Ji‐Suo Wang, 聊城师范学院物理系,聊城,252059

Published Jan 1, 1991• 4 citations
Publisher

Abstract

Based on the reference [1] , the mathematical and quantum statistical properties of the orthonormalized eigenstates of operator αk (k=3) are studied in this paper. It is found that all the orthonormalized eigenstates have nonclassical effects and they form a nonclassical complete representation. The result given by the reference [1] in the case k = 3 is only a special instance of the general conclusion of ours.

DOI
10.7498/aps.40.547

Related papers

ORTHONORMALIZED EIGENSTATES OF OPERATOR αN AND THEIR PROPERTIES

PENG SHI-AN, Guo Guang-Can, (1)河北师范学院物理系,石家庄,050091; (2)中国科学技术大学物理系,合肥,230026

In this paper, a general method for constructing orthonormalized eigenstates of operator αN is presented. The emphasis is put on study of mathematical structure and quantum statistical properties in the case N=3. It is found that all the orthonorma-lizetl eigenstates have nonclassical effects and they form a nonclassical complete representation.

Acta Physica Sinica•Jan 1, 1990•6 citations

EIGENSTATES OF OPERATOR aqN(N≥2)

Lian-Fu Wei, 四川师范大学物理系,成都610066

The orthonormal eigenstates of operator aq2 are constructed. It is shown that they form a complete Hilbert space.

Acta Physica Sinica•Jan 1, 1993•4 citations

Orthonormalized eigenstates of the quantum operator ak and their nonclassical properties

Xiao-Ming Liu, Shun-Jin Wang, ZHANG WEN-ZHONG

A method for construction of the k orthonormalized quantum eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ of the quantum-annihilation operator a is proposed, and their physical meaning is explored. Nonclassical properties of these quantum eigenstates are studied and the main results are as follows: (1) All of the eigenstates can be expressed as a linear superposition of k quantum-coherent states; (2) all of them are generalized quantum-coherent states; (3) for k\ensuremath{\ge}3, they have the Nth-order quantum squeezing for N=mk+k/2 (m=0,1,2, . . .) and even k, but no Nth-order quantum squeezing for other values of N and k; (4) for k\ensuremath{\ge}3, all of them exhibit the lowest- and higher-order quantum antibunching.

Physical Review A•Jun 1, 1995•6 citations

Orthonormalized Eigenstates of Operatorakand Their Squeezing Properties

J. Sun, Jay J. Wang, Chuan‐Kui Wang

The orthonormalized eigenstates of the higher powers, a k (k  3), of the annihilation operator a were obtained. We discuss the mathematical properties and the squeezing properties of the orthonormalized eigenstates of a k. We prove that these orthonormalized eigenstates of a k construct a complete representation, that none of them have the squeezed effect in the usual sense, and that higher-order squeezing can be found.

Journal of Modern Optics•Nov 1, 1991•9 citations

Orthonormalized eigenstates of cubic and higher powers of the annihilation operator

Jinzuo Sun, Ji‐Suo Wang, Chuan‐Kui Wang

We have studied the orthonormalized eigenstates of the higher powers ${\mathit{a}}^{\mathit{k}}$ (k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ shows the squeezing effect in the usual sense. (3) All of the eigenstates of ${\mathit{a}}^{\mathit{k}}$ show the antibunching effect.

Physical Review A•Sep 1, 1991•41 citations

Quantum statistical properties of orthonormalized eigenstates of the operator (â f ($\hat n$))k

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

The completeness of the k orthonormalized eigenstates of the operator (â f ( )) k ( k ⩾3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the M th-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and 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 an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.

Journal of Physics B Atomic Molecular and Optical Physics•May 24, 2002•12 citations
Based on the reference [1] , the mathematical and quantum statistical properties of the orthonormalized eigenstates of operator αk (k=3) are studied in this paper. It is found that all the orthonormalized eigenstates have nonclassical effects and they form a nonclassical complete representation. The result given by the reference [1] in the case k = 3 is only a special instance of the general conclusion of ours.
A method for construction of the k orthonormalized quantum eigenstates of the higher powers ak{\mathit{a}}^{\mathit{k}}ak of the quantum-annihilation operator a is proposed, and their physical meaning is explored. Nonclassical properties of these quantum eigenstates are studied and the main results are as follows: (1) All of the eigenstates can be expressed as a linear superposition of k quantum-coherent states; (2) all of them are generalized quantum-coherent states; (3) for k\ensuremath{\ge}3, they have the Nth-order quantum squeezing for N=mk+k/2 (m=0,1,2, . . .) and even k, but no Nth-order quantum squeezing for other values of N and k; (4) for k\ensuremath{\ge}3, all of them exhibit the lowest- and higher-order quantum antibunching.
We have studied the orthonormalized eigenstates of the higher powers ak{\mathit{a}}^{\mathit{k}}ak (k\ensuremath{\ge}3) of the annihilation operator a and their properties. Our conclusions are as follows: (1) The orthonormalized eigenstates of ak{\mathit{a}}^{\mathit{k}}ak construct a complete representation with respect to \ensuremath{\alpha}. (2) None of the orthonormalized eigenstates of ak{\mathit{a}}^{\mathit{k}}ak shows the squeezing effect in the usual sense. (3) All of the eigenstates of ak{\mathit{a}}^{\mathit{k}}ak show the antibunching effect.
Quantum statistical properties of orthonormalized eigenstates of the operator (â f (n^\hat nn^))k
The completeness of the k orthonormalized eigenstates of the operator (â f ( )) k ( k ⩾3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the M th-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and 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 an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.