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

Communications in Theoretical Physics

Squeezing in Representation by Quadratic Combinations ofCanonical Operators

Fan Hong-Yi, Alfred Wünsche

Published Jun 15, 2003• 6 citations
Publisher

Abstract

The technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P 2 , Q 2 , PQ + QP) to those of the basis operators (a 2 , a †2 , a † a). The coherent state representation of unitary squeezing operators in the factorized form and their normal product form are thus derived. The squeezing engendered by operators of the general form is also obtained.

DOI
10.1088/0253-6102/39/6/717

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 Representation for Squeezing-Rotating Entangled Unitary Transformation

Fan Hong-Yi, Fan Yue

We introduce a new unitary operator which can engender a squeezing and rotating entangled transformation. The operator has a concise expression in a new representation in two-mode Fock space. The normally ordered form of can be derived by using the technique of integration within an ordered product of operators. The fluctuation in quadrature phases for these squeezing-rotating entangled states are analyzed.

Communications in Theoretical Physics•Jun 15, 2000•14 citations

Coherent state representation of squeezing operator and its applications

Xiaojian Qiu, Jiali Huang, Zheng Fu +1 more

In a previous paper Zhan et al. (2022) proposed the coherent state representation for linear operator, which shows a beautiful theoretical value. Inspired by the work, we further extend it to the nonlinear case, including single- and two-mode squeezing process. Based on squeezing operators’ transformation relation, we introduce their coherent state representations and derive their normal ordering forms by using the technique of integration within product of operator. As applications, we examine some operators’s normal ordering forms and show the entanglement property of prepared quantum states via the Schmidt decomposition. In particular, we further consider two cascaded two-mode squeezing operators, in which a generalized SU(1,1) interferometer is involved. In addition, the application of two-mode squeezing operator followed by photon-subtraction to generate non-Gaussian entangled states in quantum teleportation is discussed. Our results will be useful in preparation of quantum states and quantum metrology.

Results in Physics•Nov 13, 2022•5 citations

Squeezed states: Operators for two types of one- and two-mode squeezing transformations

Fan Hong-Yi

We find that the exponential operators U=exp[-i(${\ensuremath{\lambda}}_{1}$${\mathit{Q}}_{1}$${\mathit{P}}_{2}$+${\ensuremath{\lambda}}^{2}$${\mathit{Q}}_{2}$${\mathit{P}}_{1}$] and W=exp[-i(${\ensuremath{\lambda}}_{1}$${\mathit{Q}}_{1}$${\mathit{Q}}_{2}$-${\ensuremath{\lambda}}_{2}$p${\mathrm{P}}_{1}$${\mathit{P}}_{2}$)] (where ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ are real; ${P}_{i}$ and ${Q}_{i}$ are coordinate and momentum operators, respectively; and i=1,2) are two types of generalized squeezing operators responsible for generating two types of one- and two-mode combination squeezed states, respectively. The coordinate and/or momentum representations of U and W are presented, and their normal product forms are first derived in terms of the newly developed technique of integration within an ordered product, which provides us with a direct approach to constructing these new squeezed states. The fluctuations in quadrature phases for these states are analyzed.

Physical Review A•Feb 1, 1990•88 citations

Differential-Form Relations Between Density Operators and Their P -Representations in Coherent State Basis

Hong-Yi Fan, Zhongxi Zhang

By virtue of the technique of integration within an ordered product of operators, we derive differential-form relations between density operators and their P -representations in the coherent state basis. Some applications of these new relations in normally ordering operators are given.

Communications in Theoretical Physics•Apr 30, 1996•0 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 technique of integration within an ordered product of operators and the coherent-state representation are used to convert exponential operators of basis operators (P 2 , Q 2 , PQ + QP) to those of the basis operators (a 2 , a †2 , a † a). The coherent state representation of unitary squeezing operators in the factorized form and their normal product form are thus derived. The squeezing engendered by operators of the general form is also obtained.
In a previous paper Zhan et al. (2022) proposed the coherent state representation for linear operator, which shows a beautiful theoretical value. Inspired by the work, we further extend it to the nonlinear case, including single- and two-mode squeezing process. Based on squeezing operators’ transformation relation, we introduce their coherent state representations and derive their normal ordering forms by using the technique of integration within product of operator. As applications, we examine some operators’s normal ordering forms and show the entanglement property of prepared quantum states via the Schmidt decomposition. In particular, we further consider two cascaded two-mode squeezing operators, in which a generalized SU(1,1) interferometer is involved. In addition, the application of two-mode squeezing operator followed by photon-subtraction to generate non-Gaussian entangled states in quantum teleportation is discussed. Our results will be useful in preparation of quantum states and quantum metrology.
We find that the exponential operators U=exp[-i(${\ensuremath{\lambda}}_{1}$Q1{\mathit{Q}}_{1}Q1​P2{\mathit{P}}_{2}P2​+${\ensuremath{\lambda}}^{2}$Q2{\mathit{Q}}_{2}Q2​P1{\mathit{P}}_{1}P1​] and W=exp[-i(${\ensuremath{\lambda}}_{1}$Q1{\mathit{Q}}_{1}Q1​Q2{\mathit{Q}}_{2}Q2​-${\ensuremath{\lambda}}_{2}$pP1{\mathrm{P}}_{1}P1​P2{\mathit{P}}_{2}P2​)] (where ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ are real; Pi{P}_{i}Pi​ and Qi{Q}_{i}Qi​ are coordinate and momentum operators, respectively; and i=1,2) are two types of generalized squeezing operators responsible for generating two types of one- and two-mode combination squeezed states, respectively. The coordinate and/or momentum representations of U and W are presented, and their normal product forms are first derived in terms of the newly developed technique of integration within an ordered product, which provides us with a direct approach to constructing these new squeezed states. The fluctuations in quadrature phases for these states are analyzed.
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.