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 Optica Sinica

A new formalism of the squeeze operator and various representations and properties of the squeezed state

Fan Huang, Guo Guo

Published Jan 1, 1985• 0 citations
OpenAlex

Abstract

A new formalism of the squeeze operator has been found by integration within normal ordered products. Based on this formalism, the essence of the formation of the squeezed state can be revealed directly and clearly. Various representations and properties of the squeezed state can be derived easily. It has been proved that the squeezed state is a coherent one in the quasiparticle space. The transformation relationship between squeezed states and eigenstates of both coordinate and momentum operators are presented. Also presented is the Wigner distribution function of the squeezed state.

Related papers

New approach for calculating the normally ordered form of squeeze operators

Fan Hong‐Yi, Haider R. Zaidi, John R. Klauder

A new method for directly obtaining the normally ordered form of single- and two-mode squeeze operators is presented. This method is based on the technique of ``integration within an ordered product.'' The operator expressions are derived using the coherent-state representation as well as the coordinate and the momentum representations. The method is very simple, and the approach has an intuitive basis that makes the squeezing property manifest at the outset.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Mar 15, 1987•369 citations

New n-mode squeezing operator and squeezed states with standard squeezing

Li-yun Hu, Hong-yi Fan

We find that the exponential operator V ≡exp[ i λ( Q 1 P 2 + Q 2 P 3 +⋅⋅⋅+ Q n −1 P n + Q n P 1 )], Q i , P i are, respectively, the coordinate and momentum operators, is an n -mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V 's normally ordered expansion and obtain the n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

arXiv:0902.1589•Europhysics Letters (EPL)•Mar 1, 2009•14 citations

The N -mode squeezed state with enhanced squeezing

Xue-xiang Xu, Liyun Hu, Fan Hong-Yi

It is known that exp [iλ ( Q 1 P 1 – i/2)] is a unitary single-mode squeezing operator, where Q 1 , P 1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator , is an n -mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S n 's normally ordered expansion and obtain new n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

Chinese Physics B•Dec 1, 2009•6 citations

Some New Quantum Operator Formulas—New Applications of the Coherent State

Fan Hong‐Yi, Ruan Tu-Nan

We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also

Communications in Theoretical Physics•Jul 1, 1983•10 citations

Transform relations between squeezed coherent state representation and quantum phase space distribution functions

Liang Xiu-Dong, Tai Yun-Jiao, Cheng Jian-Min +2 more

A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.

Acta Physica Sinica•Jan 1, 2015•0 citations

New application of Dirac's representation: N-mode squeezing enhanced operator and squeezed state

Xue-xiang Xu, Li-Yun Hu, Hong-Yi Fan

It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_{n}=Exp[i\lamda sum_{i=1}^{n}](Q_{i}P_{i+1}+Q_{i+1}P_{i}))], (Q_{n+1}=Q_1P_{n+1}=P_1), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_{n}'s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

arXiv:0903.0997•Mar 5, 2009•0 citations
A new formalism of the squeeze operator has been found by integration within normal ordered products. Based on this formalism, the essence of the formation of the squeezed state can be revealed directly and clearly. Various representations and properties of the squeezed state can be derived easily. It has been proved that the squeezed state is a coherent one in the quasiparticle space. The transformation relationship between squeezed states and eigenstates of both coordinate and momentum operators are presented. Also presented is the Wigner distribution function of the squeezed state.
We find that the exponential operator V ≡exp[ i λ( Q 1 P 2 + Q 2 P 3 +⋅⋅⋅+ Q n −1 P n + Q n P 1 )], Q i , P i are, respectively, the coordinate and momentum operators, is an n -mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V 's normally ordered expansion and obtain the n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
It is known that exp [iλ ( Q 1 P 1 – i/2)] is a unitary single-mode squeezing operator, where Q 1 , P 1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator , is an n -mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S n 's normally ordered expansion and obtain new n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also
A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.
It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_{n}=Exp[i\lamda sum_{i=1}^{n}](Q_{i}P_{i+1}+Q_{i+1}P_{i}))], (Q_{n+1}=Q_1P_{n+1}=P_1), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_{n}'s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.