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

Detuning effects in competing nonlinearities

Andrea Eschmann, Monika A. M. Marte

Published Apr 1, 1997• 3 citations
Publisher

Abstract

The impact of cavity detunings on the quantum noise properties of competing nonlinearities (second harmonic generation and nondegenerate optical parametric oscillation in the same cavity) is assessed. Previously predicted effects, such as sub-Poissonian pair statistics of twin photons, are shown to survive for moderate detunings of the fundamental or the second harmonic, respectively.

DOI
10.1088/1355-5111/9/2/011

Related papers

Nonlinear dynamics and quantum noise for competing χ^(2) nonlinearities

Monika A. M. Marte

The mutual influence of second-harmonic generation and nondegenerate downconversion inside the same cavity is studied. The threshold behavior and the stability of a semiclassical solution with all four modes oscillating resonantly is investigated. It is shown that under certain conditions the self-pulsing instability that occurs in second-harmonic generation is absent in the combined system. The squeezing spectra for the quadrature-phase amplitudes in the second harmonic and the fundamental, as well as the photon statistics in the downconverted modes, are derived analytically. As one of the various nonclassical features of this system, the second harmonic is found to exhibit excellent noise suppression at very large frequencies, with the frequency component of best squeezing being tunable by the pump parameter. The intricate interaction of the two nonlinear processes can give rise to twin beams of correlated photons, with sub-Poissonian statistics in each beam. These results are contrasted with the results for each nonlinear process by itself.

Journal of the Optical Society of America B•Nov 1, 1995•15 citations

Sub-Poissonian Twin Beams via Competing Nonlinearities

Monika A. M. Marte

The interaction of doubly resonant second harmonic generation and nondegenerate down-conversion in a cavity is shown to generate light with excellent noise suppression in two symmetrical dips moving away from zero frequency with increasing pump strength. This feature emerges not only in the amplitude noise of fundamental and second harmonic, but also in the single beam and the sum intensity fluctuation spectra of the twin beams produced by down-conversion, which makes this system a potentially useful source for quantum cryptography or optical quantum correlation experiments.

Physical Review Letters•Jun 12, 1995•25 citations

Quantum properties of transverse pattern formation in second-harmonic generation

Morten Bache, Pierre Scotto, Roberta Zambrini +2 more

We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.

arXiv:quant-ph/0202167•Physical Review A•Jul 19, 2002•20 citations

Nonlinear system size quantum fluctuations in optics

Christopher J. Mertens, T. A. B. Kennedy, S. Swain

Quantum properties of intracavity nonlinear optical processes such as parametric oscillation and second harmonic generation are limited to a linearized analytical treatment except for certain special cases. Perfect squeezing in one quadrature and the divergence in fluctuations of the conjugate quadrature predicted at threshold in parametric oscillation are a consequence of the approximate linearized analysis. We investigate nonlinear quantum fluctuation corrections by using nonequilibrium Green’s function methods1,2 in concert with quantum master equations, to assess when these system-size effects may be observable in the laboratory.

Annual Meeting Optical Society of America•Jan 1, 1992•0 citations

Competing nonlinearities

Monika A. M. Marte

The interaction between two cavity resonant nonlinear processes in an intracavity ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium is studied, namely frequency doubling of a pump field of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$=2${\mathrm{\ensuremath{\omega}}}_{1}$ becomes independent of the pump field ${\mathit{scrE}}_{1}$, provided ${\mathit{scrE}}_{1}$ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.

Physical Review A•May 1, 1994•33 citations

Quantum features of nonlinear coupler with competing nonlinearity

Rafael Julius, Abdel-Baset M.A. Ibrahim, P. K. Choudhury +2 more

Abstract In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.

Scientific Reports•May 17, 2022•10 citations
The impact of cavity detunings on the quantum noise properties of competing nonlinearities (second harmonic generation and nondegenerate optical parametric oscillation in the same cavity) is assessed. Previously predicted effects, such as sub-Poissonian pair statistics of twin photons, are shown to survive for moderate detunings of the fundamental or the second harmonic, respectively.
The mutual influence of second-harmonic generation and nondegenerate downconversion inside the same cavity is studied. The threshold behavior and the stability of a semiclassical solution with all four modes oscillating resonantly is investigated. It is shown that under certain conditions the self-pulsing instability that occurs in second-harmonic generation is absent in the combined system. The squeezing spectra for the quadrature-phase amplitudes in the second harmonic and the fundamental, as well as the photon statistics in the downconverted modes, are derived analytically. As one of the various nonclassical features of this system, the second harmonic is found to exhibit excellent noise suppression at very large frequencies, with the frequency component of best squeezing being tunable by the pump parameter. The intricate interaction of the two nonlinear processes can give rise to twin beams of correlated photons, with sub-Poissonian statistics in each beam. These results are contrasted with the results for each nonlinear process by itself.
The interaction of doubly resonant second harmonic generation and nondegenerate down-conversion in a cavity is shown to generate light with excellent noise suppression in two symmetrical dips moving away from zero frequency with increasing pump strength. This feature emerges not only in the amplitude noise of fundamental and second harmonic, but also in the single beam and the sum intensity fluctuation spectra of the twin beams produced by down-conversion, which makes this system a potentially useful source for quantum cryptography or optical quantum correlation experiments.
We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second-harmonic field, and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.
Quantum properties of intracavity nonlinear optical processes such as parametric oscillation and second harmonic generation are limited to a linearized analytical treatment except for certain special cases. Perfect squeezing in one quadrature and the divergence in fluctuations of the conjugate quadrature predicted at threshold in parametric oscillation are a consequence of the approximate linearized analysis. We investigate nonlinear quantum fluctuation corrections by using nonequilibrium Green’s function methods1,2 in concert with quantum master equations, to assess when these system-size effects may be observable in the laboratory.
The interaction between two cavity resonant nonlinear processes in an intracavity ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium is studied, namely frequency doubling of a pump field of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$=2${\mathrm{\ensuremath{\omega}}}_{1}$ becomes independent of the pump field scrE1{\mathit{scrE}}_{1}scrE1​, provided scrE1{\mathit{scrE}}_{1}scrE1​ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.
Abstract In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.