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

Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis

Fan Hong-Yi, Junhua Chen

Published Nov 15, 2003• 15 citations
Publisher

Abstract

We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed.

DOI
10.1088/0253-6102/40/5/589

Related papers

Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis

FANHong-Yi, Hong-Yi, Chen +1 more

We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed.

理论物理通讯：英文版•Jan 1, 2003•0 citations

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

Fan Hong-Yi, Junhua Chen

We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived.

Communications in Theoretical Physics•Aug 15, 2002•18 citations

Coherent State Projection Operator Representation of Symplectic Transformations as a Loyal Representation of Symplectic Group

Fan, Hong-Yi, Chen +1 more

We find that the coherent state projection operator representation of symplectic transformation constitutesa loyal group representation of symplectic group. The result of successively applying squeezing operators on numberstate can be easily derived.

理论物理通讯：英文版•Jan 1, 2002•0 citations

A group property for the coherent state representation of fermionic squeezing operators

Hong-Yi Fan, Chao Li

For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.

Journal of Optics B Quantum and Semiclassical Optics•May 29, 2004•4 citations

Phase Properties of Two-Mode Squeezing-Rotating Entangled Representation

Yuan Hong-Chun, Heng-Mei Li, Qi Kai-Guo

By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operator, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotating coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.

Communications in Theoretical Physics•Nov 1, 2006•1 citation

Nonlinear Squeezed States and Multiplication Rule of Nonlinear Squeezing Operators Gained via Nonlinear Coherent State Representation and IWOP Technique

FANHong-Yi, Hong-Yi, He +1 more

Using the nonlinear coherent state representation we derive nonlinear squeezed states and the multiplication rule of nonlinear squeezing operators. We find that the symplectic matrices multiplication rule in nonlinear coherent state projection operator representation maps into the multiplication rule of successive nonlinear squeezing operators.The technique of integral within an ordered product of operators plays an essential role in deriving the multiplication rule.

理论物理通讯：英文版•Jan 1, 2005•0 citations
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed.
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.
By virtue of the squeezing-rotating entangled representation, we mainly establish the new two-mode phase operator and phase angle operator, which is a general form including the foregoing formalist in two-mode Fock space. In addition, the corresponding phase distribution function is given in the entangled representation. In terms of this definition, we also analyze the phase behavior of some simple two-mode states such as squeezing-rotating coherent state, squeezing-rotating vacuum state, and so on. It is found that the results exactly agree with the foregoing phase theory.