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

Annual Meeting Optical Society of America

Quantum statistics in the nondegenerate parametric oscillator

M. D. Reid, P. D. Drummond, Alistair S. Lane, Daniel F. Walls

Published Jan 1, 1987• 0 citations
Publisher

Abstract

We study the nondegenerate parametric oscillator in the limit of small fluctuations where a linearized theory is valid. Interest is focused on solutions above threshold. It has been shown that the field undergoes phase diffusion above threshold,1 and the theory incorporates this effect. We calculate the spectrum of fluctuations in the intensity difference between the two modes,2 allowing for differing cavity mode decay rates. Possibilities for quantum nondemolition experiments and other quantum properties are discussed. In particular, the effect of phase diffusion on the long-time heterodyne squeezing spectra is calculated. The linearized results are compared to the full nonlinear steady-state solutions in the limit of a very fast decaying pump.

DOI
10.1364/oam.1987.mq9

Related papers

Quantum analysis of intensity fluctuations in the nondegenerate parametric oscillator

Alistair S. Lane, M. D. Reid, Daniel F. Walls

A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.

Physical Review A•Jul 1, 1988•74 citations

Quantum fluctuations in the optical parametric oscillator in the limit of a fast decaying subharmonic mode

Oliver Veits, Michael Fleischhauer

The quantum fluctuations in a nondegenerate optical parametric oscillator are calculated without the standard linearization assumption. Analytical results are obtained with the help of a mean-field approximation, which is exact in the limit of a fast decaying subharmonic mode. This approach is equivalent to a linearization around a self-consistently determined pump field amplitude that takes into account fluctuations of the subharmonic mode. The range of validity of the mean-field approximation is analyzed, and the influence of the system size on field amplitudes and squeezing is discussed.

Physical Review A•Dec 1, 1995•12 citations

Degenerate parametric oscillator

P. D. Drummond, Mark S. Hillery

The optical parametric oscillator is one of the most well-characterized devices in nonlinear optics, with many useful applications, especially as a frequency converter and as a wide-band amplifier. Novel discoveries made with these devices in the quantum domain include demonstrations of large amounts of both single-mode and two-mode squeezing, and, in the two-mode case, significant quantum intensity correlations between the two modes and quadrature correlations, which provided the first experimental demonstration of the original Einstein–Podolsky–Rosen (EPR) paradox. In this chapter, a systematic theory is developed of quantum fluctuations in the degenerate parametric oscillator. The quantum statistical effects produced by the degenerate parametric amplifier and oscillator have been intensely studied. As we have seen, the amount of transient squeezing produced in an ideal lossless parametric amplifier was calculated using asymptotic methods by Crouch and Braunstein. It was found to scale inversely with the square root of the initial pump photon number. When the system is put into a cavity, and driving and dissipation are introduced, we find that the steady state of a driven degenerate parametric oscillator bifurcates. There is a single steady state at low driving strengths, but, as the driving field increases, a threshold value is reached and the single state splits and forms two stable states. Below the threshold, a linearized analysis of squeezing in the quantum quadratures is possible; while above this threshold, or critical point, the tunneling time between the two states due to quantum fluctuations can be calculated.

Cambridge University Press eBooks•Mar 27, 2014•0 citations

Influence of pump-phase fluctuations on the squeezing in a degenerate parametric oscillator

Julio R. Gea-Banacloche, Muhammad Suhail Zubairy

The fluctuations in the phase of the pump in a degenerate optical parametric oscillator are modeled by a classical phase-diffusion process, and their influence on squeezing is studied. To this end, appropriate quadrature variables, relative to the instantaneous phase of the pump, are introduced. The squeezing is calculated both inside and outside the cavity. In both cases it is found to be degraded by the phase fluctuations, which may be understood in terms of the time lag in the response of the system to an instantaneous change in the pump phase. This effect might account for a small part of the residual noise present in current experiments. Correlation functions for the field of the oscillator for finite pump linewidth are derived and discussed.

Physical Review A•Aug 1, 1990•20 citations

Correlations in nondegenerate parametric oscillation: Squeezing in the presence of phase diffusion

M. D. Reid, P. D. Drummond

We present a quantum theory of the nondegenerate parametric oscillator above threshold. The effect of signal and idler phase diffusion on the various types of external squeezing spectral measurements is discussed.

Physical Review A•Oct 1, 1989•125 citations

Isotropic and squeezed colored pump noise effects on the degenerate parametric oscillator

L. Gilles, P. Tombesi, Maxi San Miguel +1 more

The degenerate parametric oscillator above threshold is studied with phenomenological stochastic colored (nonwhite) pump noise for arbitrary pump to subharmonic relaxation rate. The current experimental limits of large intracavity threshold photon numbers (very small quantum noise) are considered, allowing for a semiclassical treatment of the system dynamics. A comparison between the effects of isotropic and squeezed pump noise on the internal transient and steady-state fluctuations is presented by simulation of the nonlinear semiclassical stochastic Langevin equations in the Wigner quadrature representation. It is found that the transient squeezing for the system starting in the unstable steady state (the vacuum) is not degraded by stochastic pump noise. A damped oscillatory behavior of the noise levels (periodic exchange of fluctuations between the squeezed quadrature of the signal and the pump) is observed for large damping of the signal in the turn on of pump depletion. Finally, it is shown that the limited squeezing above threshold in the steady state (50%) due to pump depletion can be enhanced if squeezed stochastic noise with sufficient significant spectral components (broadband squeezing) is fed to the pump. The above-threshold steady-state squeezing has been calculated analytically from the linearized stochastic equations and the effects of the time scale associated to the relaxation of the pump noise (the noise correlation time) compared to the dissipative time scale of the system and the pump to subharmonic loss ratio are presented.

Physical Review A•Mar 1, 1997•6 citations
We study the nondegenerate parametric oscillator in the limit of small fluctuations where a linearized theory is valid. Interest is focused on solutions above threshold. It has been shown that the field undergoes phase diffusion above threshold,1 and the theory incorporates this effect. We calculate the spectrum of fluctuations in the intensity difference between the two modes,2 allowing for differing cavity mode decay rates. Possibilities for quantum nondemolition experiments and other quantum properties are discussed. In particular, the effect of phase diffusion on the long-time heterodyne squeezing spectra is calculated. The linearized results are compared to the full nonlinear steady-state solutions in the limit of a very fast decaying pump.
A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.
The quantum fluctuations in a nondegenerate optical parametric oscillator are calculated without the standard linearization assumption. Analytical results are obtained with the help of a mean-field approximation, which is exact in the limit of a fast decaying subharmonic mode. This approach is equivalent to a linearization around a self-consistently determined pump field amplitude that takes into account fluctuations of the subharmonic mode. The range of validity of the mean-field approximation is analyzed, and the influence of the system size on field amplitudes and squeezing is discussed.
The optical parametric oscillator is one of the most well-characterized devices in nonlinear optics, with many useful applications, especially as a frequency converter and as a wide-band amplifier. Novel discoveries made with these devices in the quantum domain include demonstrations of large amounts of both single-mode and two-mode squeezing, and, in the two-mode case, significant quantum intensity correlations between the two modes and quadrature correlations, which provided the first experimental demonstration of the original Einstein–Podolsky–Rosen (EPR) paradox. In this chapter, a systematic theory is developed of quantum fluctuations in the degenerate parametric oscillator. The quantum statistical effects produced by the degenerate parametric amplifier and oscillator have been intensely studied. As we have seen, the amount of transient squeezing produced in an ideal lossless parametric amplifier was calculated using asymptotic methods by Crouch and Braunstein. It was found to scale inversely with the square root of the initial pump photon number. When the system is put into a cavity, and driving and dissipation are introduced, we find that the steady state of a driven degenerate parametric oscillator bifurcates. There is a single steady state at low driving strengths, but, as the driving field increases, a threshold value is reached and the single state splits and forms two stable states. Below the threshold, a linearized analysis of squeezing in the quantum quadratures is possible; while above this threshold, or critical point, the tunneling time between the two states due to quantum fluctuations can be calculated.
The fluctuations in the phase of the pump in a degenerate optical parametric oscillator are modeled by a classical phase-diffusion process, and their influence on squeezing is studied. To this end, appropriate quadrature variables, relative to the instantaneous phase of the pump, are introduced. The squeezing is calculated both inside and outside the cavity. In both cases it is found to be degraded by the phase fluctuations, which may be understood in terms of the time lag in the response of the system to an instantaneous change in the pump phase. This effect might account for a small part of the residual noise present in current experiments. Correlation functions for the field of the oscillator for finite pump linewidth are derived and discussed.
The degenerate parametric oscillator above threshold is studied with phenomenological stochastic colored (nonwhite) pump noise for arbitrary pump to subharmonic relaxation rate. The current experimental limits of large intracavity threshold photon numbers (very small quantum noise) are considered, allowing for a semiclassical treatment of the system dynamics. A comparison between the effects of isotropic and squeezed pump noise on the internal transient and steady-state fluctuations is presented by simulation of the nonlinear semiclassical stochastic Langevin equations in the Wigner quadrature representation. It is found that the transient squeezing for the system starting in the unstable steady state (the vacuum) is not degraded by stochastic pump noise. A damped oscillatory behavior of the noise levels (periodic exchange of fluctuations between the squeezed quadrature of the signal and the pump) is observed for large damping of the signal in the turn on of pump depletion. Finally, it is shown that the limited squeezing above threshold in the steady state (50%) due to pump depletion can be enhanced if squeezed stochastic noise with sufficient significant spectral components (broadband squeezing) is fed to the pump. The above-threshold steady-state squeezing has been calculated analytically from the linearized stochastic equations and the effects of the time scale associated to the relaxation of the pump noise (the noise correlation time) compared to the dissipative time scale of the system and the pump to subharmonic loss ratio are presented.