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

Modern Physics Letters B

SQUEEZING ENHANCED THREE-MODE ENTANGLED STATE

Liyun Hu, Hong-Yi Fan

Published Aug 30, 2008• 2 citations
Publisher

Abstract

By virtue of the technique of integration within an ordered product of operators (Fan et al., Ann. Phys.321 (2006) 480) we construct a kind of three-mode entangled squeezed state in the Fock space, which exhibits stronger squeezing in one quadrature than that of the usual two-mode squeezed vacuum state.
DOI
10.1142/s0217984908016662

Related papers

Three-mode squeezed vacuum state in Fock space as an entangled state

Hong-Yi Fan, Guichuan Yu

We show that the operator $U=\mathrm{exp}[\ensuremath{-}{ir(Q}_{1}{P}_{2}{+Q}_{2}{P}_{3}{+Q}_{3}{P}_{1})]$ is a three-mode squeezing operator for the three-mode quadratures exhibiting the standard squeezing, the corresponding squeezed vacuum state in three-mode Fock space is derived by virtue of the technique of integration within ordered product of operators. The entanglement involved in such a state is explained. The optical network for producing the three-mode squeezed state is proposed.

Physical Review A•Feb 28, 2002•21 citations

New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing

Xue-xiang Xu, Hong-Yi Fan, Liyun Hu +1 more

In a 3-wave mixing process occurring in some nonlinear optical medium when }$a_{1}^{\dagger}${\small mode interacts with both }$a_{2}^{\dagger}% ${\small mode and }$a_{3}^{\dagger}${\small mode, we theoretically study the squeezing effect generated by the operator }$S_{3}\equiv \exp[μ(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+ν(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})]${\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }$S_{3}${\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }$S_{3}${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.

arXiv:1009.2548•Sep 14, 2010•0 citations

Squeezing Transformation of Three-Mode Entangled State

Xiao-Qing Qian, Song Tong-Qiang

We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed | p , χ 2 , χ 3 ⟩ → μ -3/2 | p /μ, χ 2 /μ, χ 3 /μ ⟩ and the optical implement to realize such a squeezed state. We also reveal that c -number asymmetric shrink transform in the three-mode entangled state, i.e. | p , χ 2 , χ 3 ⟩ → μ -1/2 | p /μ, χ 2 , χ 3 ⟩, maps onto a kind of one-sided three-mode squeezing operator exp {iλ/3 (∑ i =1 3 P i ) (∑ i =1 3 Q i ) − λ/2}. Using the technique of integration within an ordered product (IWOP) of operators, we derive their normally ordered forms and construct the corresponding squeezed states.

Communications in Theoretical Physics•Nov 1, 2005•1 citation

The higher-order squeezing for one- and two-mode combination squeezed states

Zhongxi Zhang, Fan Hong‐Yi

The one- and two-mode combination squeezed states are constructed by applying the operator U identical to exp(-i lambda (erQ1P2+e-rQ2P1)) or W identical to exp(-i lambda (erQ1Q2-e-rP1P2)) (where lambda , r are real; Qi, Pi, i=1, 2 are coordinate and momentum operators, respectively) to the vacuum state. When the condition tanh lambda <1/(1+cosh r) is satisfied, such states can have less fluctuations in one quadrature phase than the usual two-mode squeezed state. Here, the authors examine the higher-order squeezing properties for such states. The result shows that under the same conditions, these states can exhibit a stronger form of higher-order squeezing than the usual two-mode squeezed state.

Quantum Optics Journal of the European Optical Society Part B•Jun 1, 1993•1 citation

Three-Mode Squeezing Operators

Fan Hong‐Yi, Shen-xi Yu

We search for squeezing operator which squeezes the two quadratures for three-mode optical field as the behavior of single-mode case. The normally ordered form of the squeezing operator is also obtained by virtue of the technique of integration within an ordered product of operators.

Communications in Theoretical Physics•Jun 15, 1998•0 citations

Three-Mode Cyclic Squeezed States Constructed via EPR Entangled State

Xuefen Xu

We construct the three-mode cyclic squeezed states and analyze its squeezing property by using the technique of integration within an ordered product of operators and the natural representation of the two-mode squeezing operator in the Einstein–Podolsky–Rosen entangled state basis.

Communications in Theoretical Physics•May 1, 2007•1 citation
We show that the operator $U=\mathrm{exp}[\ensuremath{-}{ir(Q}_{1}{P}_{2}{+Q}_{2}{P}_{3}{+Q}_{3}{P}_{1})]$ is a three-mode squeezing operator for the three-mode quadratures exhibiting the standard squeezing, the corresponding squeezed vacuum state in three-mode Fock space is derived by virtue of the technique of integration within ordered product of operators. The entanglement involved in such a state is explained. The optical network for producing the three-mode squeezed state is proposed.
In a 3-wave mixing process occurring in some nonlinear optical medium when }a1†a_{1}^{\dagger}a1†​{\small mode interacts with both }$a_{2}^{\dagger}% modeand{\small mode and }modeanda_{3}^{\dagger}mode,wetheoreticallystudythesqueezingeffectgeneratedbytheoperator{\small mode, we theoretically study the squeezing effect generated by the operator }mode,wetheoreticallystudythesqueezingeffectgeneratedbytheoperatorS_{3}\equiv \exp[μ(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+ν(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})].Thenew3−modesqueezedvacuumstateinFockspaceisderived,andtheuncertaintyrelationforitisdemonstrated,Itturnsoutthat{\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }.Thenew3−modesqueezedvacuumstateinFockspaceisderived,andtheuncertaintyrelationforitisdemonstrated,ItturnsoutthatS_{3}mayexhibitenhancedsqueezing.Byvirtueofthetechniqueofintegrationwithinanorderedproduct(IWOP)ofoperators,wealsoderive{\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }mayexhibitenhancedsqueezing.Byvirtueofthetechniqueofintegrationwithinanorderedproduct(IWOP)ofoperators,wealsoderiveS_{3}${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.
We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed | p , χ 2 , χ 3 ⟩ → μ -3/2 | p /μ, χ 2 /μ, χ 3 /μ ⟩ and the optical implement to realize such a squeezed state. We also reveal that c -number asymmetric shrink transform in the three-mode entangled state, i.e. | p , χ 2 , χ 3 ⟩ → μ -1/2 | p /μ, χ 2 , χ 3 ⟩, maps onto a kind of one-sided three-mode squeezing operator exp {iλ/3 (∑ i =1 3 P i ) (∑ i =1 3 Q i ) − λ/2}. Using the technique of integration within an ordered product (IWOP) of operators, we derive their normally ordered forms and construct the corresponding squeezed states.
The one- and two-mode combination squeezed states are constructed by applying the operator U identical to exp(-i lambda (erQ1P2+e-rQ2P1)) or W identical to exp(-i lambda (erQ1Q2-e-rP1P2)) (where lambda , r are real; Qi, Pi, i=1, 2 are coordinate and momentum operators, respectively) to the vacuum state. When the condition tanh lambda <1/(1+cosh r) is satisfied, such states can have less fluctuations in one quadrature phase than the usual two-mode squeezed state. Here, the authors examine the higher-order squeezing properties for such states. The result shows that under the same conditions, these states can exhibit a stronger form of higher-order squeezing than the usual two-mode squeezed state.