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

Chinese Physics B

The N -mode squeezed state with enhanced squeezing

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

Published Dec 1, 2009• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/18/12/007

Related papers

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

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

New Normally Ordered Four-Mode Squeezing Operator for Standard Squeezing of Four-Mode Quadratures

Fan Hong-Yi, Cao He-Lin

By virtue of the technique of integration within an ordered product of operators a new four-mode squeezing operator that squeezes the four-mode quadrature operators of light field in the standard way is found. This operator differs from the direct product of two two-mode squeezing operators. It is the exponential operator V ≡exp [ i r ( Q 1 P 2 + Q 2 P 3 + Q 3 P 4 + Q 4 P 1 )]. The Wigner function of the new four-mode squeezed state is calculated, which quite differs from that of the direct-product state of two usual two-mode squeezed states.

Communications in Theoretical Physics•Jan 1, 2007•1 citation

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

New approach for obtaining the squeezing-enhanced state and its Wigner function by virtue of the Weyl–Wigner quantization scheme

Hong-Yi Fan, Hong‐Chun Yuan, Xue-xiang Xu +1 more

By virtue of the Weyl?Wigner quantization scheme, we derive the explicit form of the squeezing-enhanced state without disentangling the generalized squeezing operator where Q and P are two quadratures of the light field; this approach is convenient and concise. By virtue of the Weyl-ordering invariance under similar transformations, the Wigner function of the squeezing-enhanced state is derived and its figure is depicted, which clearly exhibits the squeezing enhancement.

Physica Scripta•Jan 1, 2011•8 citations

One- and two-mode successively squeezed state and its statistical properties

Yuan Hong-Chun, Xue-xiang Xu

One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.

Acta Physica Sinica•Jan 1, 2012•4 citations
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 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[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.
By virtue of the technique of integration within an ordered product of operators a new four-mode squeezing operator that squeezes the four-mode quadrature operators of light field in the standard way is found. This operator differs from the direct product of two two-mode squeezing operators. It is the exponential operator V ≡exp [ i r ( Q 1 P 2 + Q 2 P 3 + Q 3 P 4 + Q 4 P 1 )]. The Wigner function of the new four-mode squeezed state is calculated, which quite differs from that of the direct-product state of two usual two-mode squeezed states.
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.
One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.