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From Wigner hyperbolic rotation to fractional squeezing transformation
Wei-Feng Wu1,2,3, Peng Fu1,2, Hua-Kui Hu1,3
1School of Mechanical and Electrical Engineering, Chizhou University, Chizhou 247000, Anhui, China.
Heliyon
|March 21, 2024
Summary
Wigner hyperbolic rotation in phase space is shown to correspond to fractional squeezing operators in Hilbert space. This finding utilizes Weyl ordering and coherent state representations of the Fresnel operator.
Area of Science:
- Quantum optics
- Mathematical physics
Background:
- The Wigner-Weyl transformation provides a framework for analyzing quantum systems in phase space.
- Fractional quantum mechanics and squeezing operators are key concepts in quantum information and optics.
Purpose of the Study:
- To establish a connection between Wigner hyperbolic rotations in phase space and fractional squeezing operators in Hilbert space.
- To explore the application of Weyl ordering and coherent state representations in this context.
Main Methods:
- Utilizing the standard Wigner-Weyl transformation theory.
- Applying the principles of Weyl ordering.
- Employing the coherent state representation of the Fresnel operator.
Main Results:
- Demonstrated that Wigner hyperbolic rotation in phase space maps to fractional squeezing operators in Hilbert space.
- The derivation leverages the properties of Weyl ordering and coherent states.
Conclusions:
- The study provides a novel link between phase space transformations and quantum optical operators.
- This work offers a new perspective on fractional squeezing and its generation through phase space manipulations.
Keywords:
Coherent state representationIWOP methodWeyl orderingWigner hyperbolic rotationWigner-Weyl transformation theoryMore Related Videos
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