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

Journal of Modern Optics

Quantum travelling-wave analysis of a quasi-phase-matched parametric amplifier

Chao Zhao, W. H. Tan

Published Mar 1, 2006• 1 citation
Publisher

Abstract

The paper describes a phase-mismatched Fokker–Planck equation formulation for parametric amplification in periodically inverted nonlinear media. An analytical solution of the phase-mismatched Fokker–Planck equation and the amplitude quantum fluctuation after passing through the quasi-phase-matched (QPM) device are obtained. The calculated results for the QPM device conform to that of the Langevin equation in the case of no loss k=0, and give a general solution for k≠0. From this one can derive knowledge of the dependence of squeezing on the loss coefficient k and make a comparison between the QPM device and a phase matched device at the threshold k=ε0.

DOI
10.1080/09500340500474669

Related papers

The solution of phase-mismatched Fokker-Planck equation and its application in the QPM device

Chao Zhao, TAN WEI-HAN, 上海大学物理系,上海 200444

A new analytical solution for the phase_mismatched Fokker_Planck equation of deg enerate parametric amplification, and its application in evaluation of the ampli tude quantum fluctuation after passing through the quasi_phase_matching(QPM) dev ice is presented. The calculated results for QPM device, agree with that of the Langevin equation in the case of no loss k=0, and give a general solution fo r k≠0, from which we can derive the influence of squeezing on the loss coef ficient k.

Acta Physica Sinica•Jan 1, 2005•0 citations

The tripartite entanglement in a phase-mismatched frequency non-degenerated optical parametric amplifier

Chao Zhao

We present an analytical solution for Fokker–Planck equation of phase-mismatched frequency non-degenerated optical parametric amplifier (FNOPA). We investigate the continuous-variable (CV) tripartite entanglement characteristic of FNOPA working at phase-matched and phase-mismatched condition. From below threshold to above threshold, we numerically calculate the dependence of CV tripartite entanglement on relative loss parameter η and phase-mismatched factor Δω. The larger η and the smaller Δω can bring a good entanglement.

Journal of Modern Optics•Aug 2, 2016•1 citation

Quantum noise reduction in quasi-phase-matched optical parametric amplification

Kamel Bencheikh, E. Huntziger, Juan Ariel Levenson

We present a calculation of quantum noise for parametric amplification in periodically inverted nonlinear media. An analytical expression is obtained for the noise figure of the amplifier. We show that such optical parametric amplifiers run in a phase-sensitive configuration can achieve noiseless amplification and squeezing, thus constituting a promising way for the integration of noiseless optical amplifiers in a communication line.

Journal of the Optical Society of America B•May 1, 1995•31 citations

Quantum fluctuation of nonlinear degenerate optical parametric amplification

Chao Zhao, W. H. Tan

An analytical solution of the Fokker–Planck equation for the nonlinear degenerate optical parametric amplifier (DOPA) is presented, taking into account the influence of pump depletion on the generation of squeezed light. Results conform to those obtained using perturbation series expansion theory near threshold, and also apply to the whole region far away from threshold. When the nonlinear term(η → 0) is neglected, the solution transitions naturally to the linear approximation solution; when the nonlinear term is retained (∞ η), in the case μ → 0, the quantum fluctuations are close to vacuum fluctuations; in the case μ ≫ 1, squeezing increases, and tends to the result obtained using linear theory, 1/(1 + μ).

Journal of Modern Optics•Jun 27, 2006•5 citations

Quantum wideband traveling-wave analysis of a degenerate parametric amplifier

Carlton M. Caves, David D. Crouch

We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations—spatial Langevin equations—that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier.

Journal of the Optical Society of America B•Oct 1, 1987•132 citations

A Theoretical Study of the Generation of Squeezed-State Light via Degenerate Parametric Amplification

David D. Crouch

This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.

•Nov 21, 2007•0 citations
The paper describes a phase-mismatched Fokker–Planck equation formulation for parametric amplification in periodically inverted nonlinear media. An analytical solution of the phase-mismatched Fokker–Planck equation and the amplitude quantum fluctuation after passing through the quasi-phase-matched (QPM) device are obtained. The calculated results for the QPM device conform to that of the Langevin equation in the case of no loss k=0, and give a general solution for k≠0. From this one can derive knowledge of the dependence of squeezing on the loss coefficient k and make a comparison between the QPM device and a phase matched device at the threshold k=ε0.
We present an analytical solution for Fokker–Planck equation of phase-mismatched frequency non-degenerated optical parametric amplifier (FNOPA). We investigate the continuous-variable (CV) tripartite entanglement characteristic of FNOPA working at phase-matched and phase-mismatched condition. From below threshold to above threshold, we numerically calculate the dependence of CV tripartite entanglement on relative loss parameter η and phase-mismatched factor Δω. The larger η and the smaller Δω can bring a good entanglement.
An analytical solution of the Fokker–Planck equation for the nonlinear degenerate optical parametric amplifier (DOPA) is presented, taking into account the influence of pump depletion on the generation of squeezed light. Results conform to those obtained using perturbation series expansion theory near threshold, and also apply to the whole region far away from threshold. When the nonlinear term(η → 0) is neglected, the solution transitions naturally to the linear approximation solution; when the nonlinear term is retained (∞ η), in the case μ → 0, the quantum fluctuations are close to vacuum fluctuations; in the case μ ≫ 1, squeezing increases, and tends to the result obtained using linear theory, 1/(1 + μ).
We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations—spatial Langevin equations—that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.