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

One dimensional representations in quantum optics

Foldesi, I., Janszky, J., Adam, P., Vinogradov, An. V.

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.

Related papers

One dimensional representations in quantum optics

József Janszky

As a generalization of the optical Schroedinger cats discrete and continuous sets of coherent states are considered on a circle and on a straight line in the a-plane. The interference fringes between the coherent states of the Schroedinger cats form the characteristic pattern of the nonclassical states in Wigner function picture. Continuos superpositions of coherent states on these one-dimensional manifolds can serve as an orthonormal basis for representation of any states.

16th Congress of the International Commission for Optics: Optics as a Key to High Technology•Jul 26, 1993•0 citations

Coherent states on a circle and quantum interference

József Janszky, P. Domokos, Петер Адам

As a generalization of the optical Schr\"odinger cats, discrete sets of coherent states are considered on a circle in the \ensuremath{\alpha} plane. It is shown that simple superpositions of Schr\"odinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state.

Physical Review A•Sep 1, 1993•120 citations

Notes on squeezed states in x-space representation

Alexander N. Korotkov

In these notes, we discuss squeezed states using the elementary quantum language based on one-dimensional Schrödinger equation. No operators are used. The language of quantum optics is mentioned only for a hint to solve a differential equation. Sections II and III (squeezed vacuum and pure squeezed states) can be used in a standard undergraduate course on quantum mechanics after discussion of a harmonic oscillator. Section IV discusses density matrix of mixed squeezed states in $x$-representation. These notes present explicit (therefore somewhat lengthy) step-by-step derivations. These notes are not intended for publication as a journal paper.

arXiv:1809.05531•Sep 14, 2018•0 citations

A non-Gaussian single-mode squeezed state of the simple harmonic oscillator

C V Sukumar

A unitary operator U R , which generates a single-mode squeezed state of the simple harmonic oscillator from the vacuum, is discussed. The states generated by U R are of the form psi 0 ( alpha ) approximately Sigma n alpha n mod n). psi 0 ( alpha ) are not minimum-uncertainty states but have a small value for the uncertainty product even for large values of the mean number of quanta n; for example, var(q) var(p) approximately 0.74 for n=10 6 .

Journal of Physics A Mathematical and General•Nov 21, 1988•8 citations

Displacement and Squeeze Operators of a Three-Dimensional Harmonic Oscillator and Their Associated Quantum States

Mehdi Miri, Sina Ataollah Khorasani

We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated the Wigner function for the three-dimensional harmonic oscillator and from the analysis of time evolution of this function, the quantum Liouville equation is also presented. Further properties of the quantum states including Mandel's Q and quadrature squeezing parameters are discussed as well.

arXiv:0912.3335•International Journal of Optics and Photonics•Dec 17, 2009•0 citations

On the Quantum Mechanics of Squeezed States

K. Wódkiewicz

We show that the squeezed states of quantum optics are physically and mathematically equivalent to Gaussian wave packets. In the framework of wave mechanics it is possible to formulate and investigate in a very simple way all the properties of reduced or squeezed fluctuations of the position and momentum operators. We study squeezed quantum fluctuations of a minimum-uncertainty Gaussian wave function under two different dynamical conditions of free evolution and harmonic oscillation.

Journal of Modern Optics•Jun 1, 1987•37 citations
The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.
As a generalization of the optical Schr\"odinger cats, discrete sets of coherent states are considered on a circle in the \ensuremath{\alpha} plane. It is shown that simple superpositions of Schr\"odinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state.
In these notes, we discuss squeezed states using the elementary quantum language based on one-dimensional Schrödinger equation. No operators are used. The language of quantum optics is mentioned only for a hint to solve a differential equation. Sections II and III (squeezed vacuum and pure squeezed states) can be used in a standard undergraduate course on quantum mechanics after discussion of a harmonic oscillator. Section IV discusses density matrix of mixed squeezed states in xxx-representation. These notes present explicit (therefore somewhat lengthy) step-by-step derivations. These notes are not intended for publication as a journal paper.
We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated the Wigner function for the three-dimensional harmonic oscillator and from the analysis of time evolution of this function, the quantum Liouville equation is also presented. Further properties of the quantum states including Mandel's Q and quadrature squeezing parameters are discussed as well.