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

Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Global characteristics of the dynamics of degenerate parametric nonlinear processes

Ondřej Haderka, J. Bajer, Jan Peřina

Published Dec 1, 1996• 3 citations
Publisher

Abstract

A new method for characterization of the long-time dynamics of generation of second and higher harmonics and subharmonics is presented. This method is based on calculation of the spectra of moments of photon numbers and enables us to predict the global behaviour of the process. This is demonstrated by numerical results, which are discussed and related to the time-domain dynamics and to short-time analytical results.

DOI
10.1088/1355-5111/8/6/005

Related papers

Photon statistics of higher harmonics and subharmonics generation

J. Bajer, Tomáš Opatrný, Jan Peřina

The quantum statistics of higher harmonics and subharmonics generation processes is studied in an exact way. By means of the described numerical way the Q-distributions and Wigner distributions are calculated and presented. The non-classical effects are examined and corresponding relations are derived.

Quantum Optics Journal of the European Optical Society Part B•Oct 1, 1994•6 citations

Quantum phase properties of impeded second-harmonic generation

Vlasta Peřinová, A. Lukš, J. Křepelka

Using the statistical characteristics of the photon number, quantum phase and field quadratures, based on the preferred phase, we have demonstrated a Kerr-like behaviour for the cascaded second-order nonlinearities and have studied thoroughly the oscillations superimposed on the Kerr-like trend for an input coherent state. We have performed a global study over the entire quantum period in an idealized model of the trend of this process based on the lossless Kerr progression.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Apr 1, 1998•2 citations

Symbolic Computation Approach to Nonlinear Dynamics

J. Bajer, Petr Lisoněk

The description and demonstration of a short-time approximation method are presented for solution of the Heisenberg equation using a computer for operator algebra symbolic computation to obtain an operator series. Multimode nonlinear processes can be studied by this method in a fully quantum way; the symbolic operator or standard numerical results as well as the graphical dependences can be computed. Although a use for the method can be seen in its ability to improve numerical predictions rather than to discover new states or effects, we have obtained squeezing parameters and variances of photon number for initially squeezed states (and some other cases) in degenerate parametric processes.

Journal of Modern Optics•Apr 1, 1991•9 citations

Sub-Poissonian behaviour in the second harmonic generation

JiríBajer, Ondřej Haderka, Jan Peřina

A special class of quantum solutions of the second harmonic generation process exhibiting time-stable sub-Poissonian behaviour with Fano factor F 0.83 is numerically analysed. A theoretical prediction of that specific Fano number and an explanation of the extraordinary time stability of the sub-Poissonian behaviour is given using the semiclassical method of classical trajectories.

Journal of Optics B Quantum and Semiclassical Optics•Aug 13, 1999•12 citations

Quantum, classical and semiclassical analyses of photon statistics in harmonic generation

J. Bajer, Adam Miranowicz

In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the third harmonic equal to 13/16.

arXiv:quant-ph/0109075•Sep 15, 2001•0 citations

Second Harmonic Revisited: An Analytic Quantum Approach

Giovanni Chesi, Matteo M. Wauters, Nadir Fasola +2 more

We address the second-harmonic generation process in a quantum frame. Starting with a perturbative approach, we show that it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties of the generated light. In particular, the moments and the correlations of the photon-number distribution of the second-harmonic light generated by any initial state are retrieved. When possible, a comparison with the results achieved with the classical regime is successfully provided. The nonclassicality of some benchmark states is investigated by inspecting the corresponding autocorrelation function.

Applied Sciences•Apr 24, 2019•10 citations
A new method for characterization of the long-time dynamics of generation of second and higher harmonics and subharmonics is presented. This method is based on calculation of the spectra of moments of photon numbers and enables us to predict the global behaviour of the process. This is demonstrated by numerical results, which are discussed and related to the time-domain dynamics and to short-time analytical results.
The description and demonstration of a short-time approximation method are presented for solution of the Heisenberg equation using a computer for operator algebra symbolic computation to obtain an operator series. Multimode nonlinear processes can be studied by this method in a fully quantum way; the symbolic operator or standard numerical results as well as the graphical dependences can be computed. Although a use for the method can be seen in its ability to improve numerical predictions rather than to discover new states or effects, we have obtained squeezing parameters and variances of photon number for initially squeezed states (and some other cases) in degenerate parametric processes.
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the third harmonic equal to 13/16.
We address the second-harmonic generation process in a quantum frame. Starting with a perturbative approach, we show that it is possible to achieve a number of analytic results, ranging from the up-conversion probability to the statistical properties of the generated light. In particular, the moments and the correlations of the photon-number distribution of the second-harmonic light generated by any initial state are retrieved. When possible, a comparison with the results achieved with the classical regime is successfully provided. The nonclassicality of some benchmark states is investigated by inspecting the corresponding autocorrelation function.