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

Optics Communications

Wave-function transformations by general SU(1,1) single-mode squeezing and analogy to Fresnel transformations in wave optics

Hong-Yi Fan, Lu Hai-Liang

Published Aug 9, 2005• 25 citations
Publisher
DOI
10.1016/j.optcom.2005.07.044

Related papers

Optical Fresnel Transform as a Correspondence of the SU(1,1) Squeezing Operator Composed of Quadratic Combination of Canonical Operators and the Entangled State

Hong-Yi Fan, Hai-liang Lu

International Journal of Theoretical Physics•Mar 1, 2006•5 citations

Generalized Fresnel operators corresponding to optical Fresnel diffraction and the squeezed states

Hongqi Li, Ting-Qi Ren

Science China Physics Mechanics and Astronomy•May 3, 2012•0 citations

Spectra and Generalized Eigenfunctions of the One- and Two-Mode Squeezing Operators in Quantum Optics

Bengt Nagel

Springer eBooks•Jan 1, 1995•10 citations

Adaption of optical Fresnel transform to optical Wigner transform

Cui-hong Lv, Hong-Yi Fan

Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.

Physica Scripta•Jul 29, 2010•1 citation

On the Phase-Space Approach to Squeezed Phenomena in Quantum Optics

Arkadiusz Orłowski, K. Wódkiewicz

Springer eBooks•Jan 1, 1990•0 citations

Squeezed-state wave functions and their relation to classical phase-space maps

Fan Hong‐Yi, Jack Vanderlinde

Coordinate wave functions for the one-mode squeezed states produced by the quantum analog of the general linear transformation in phase space are calculated. The probability density [\ensuremath{\Vert}\ensuremath{\psi}(q)${\ensuremath{\Vert}}^{2}$] for these states is Gaussian with center predicted by the classical transformation. The quantum image (which includes the traditional two-mode squeeze operator) of a three-parameter symplectic map in two-mode phase space equally generates squeezed states having Gaussian \ensuremath{\Vert}\ensuremath{\psi}(${q}_{1}$,${q}_{1}$)${\ensuremath{\Vert}}^{2}$. The center of the two-mode Gaussian is again predicted by the classical mapping.

Physical Review A•Oct 1, 1989•19 citations
Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.
Coordinate wave functions for the one-mode squeezed states produced by the quantum analog of the general linear transformation in phase space are calculated. The probability density [\ensuremath{\Vert}\ensuremath{\psi}(q)${\ensuremath{\Vert}}^{2}$] for these states is Gaussian with center predicted by the classical transformation. The quantum image (which includes the traditional two-mode squeeze operator) of a three-parameter symplectic map in two-mode phase space equally generates squeezed states having Gaussian \ensuremath{\Vert}\ensuremath{\psi}(q1{q}_{1}q1​,q1{q}_{1}q1​)${\ensuremath{\Vert}}^{2}$. The center of the two-mode Gaussian is again predicted by the classical mapping.