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Journal of the Optical Society of America B

Quantum fluctuations in a two-mode parametric oscillator

Serge Reynaud, Claude Fabre, E. Giacobino

Published Oct 1, 1987• 197 citations
Publisher

Abstract

We describe how a two-mode, above-threshold, optical parametric oscillator can generate nonclassical states of light with a large average number of photons: the fluctuation spectrum of the various fields is calculated, and several quantities are shown to have squeezed fluctuations. In particular, a perfect quantum noise suppression is predicted on the difference between the intensities of the two generated beams. We describe an experiment designed to demonstrate such an effect and show how it can be used to generate high-intensity amplitude-squeezed states.

DOI
10.1364/josab.4.001520

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We describe how a two-mode, above-threshold, optical parametric oscillator can generate nonclassical states of light with a large average number of photons: the fluctuation spectrum of the various fields is calculated, and several quantities are shown to have squeezed fluctuations. In particular, a perfect quantum noise suppression is predicted on the difference between the intensities of the two generated beams. We describe an experiment designed to demonstrate such an effect and show how it can be used to generate high-intensity amplitude-squeezed states.
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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.
We show that an optical parametric oscillator which is simultaneously resonant for several modes, either spatial or temporal, generates both below and above threshold a multimode nonclassical state of light consisting of squeezed vacuum states in all the nonoscillating modes. We confirm this prediction by an experiment dealing with the degenerate TEM01{}_{01}01​ and TEM10{}_{10}10​ modes. We show the conservation of nonclassical properties when the threshold is crossed. The experiment is made possible by the implementation of a new method to lock the relative phase of the pump and the injected beam.
We perform a theoretical analysis of steady-state solutions and quantum noise in a below-threshold optical parametric oscillator (OPO) operating as an amplifier with an input seed wave. Both the amplitude-squeezed and phase-squeezed states of the output field are considered. We take into account the intracavity nonlinear losses due to intracavity frequency doubling of the signal wave and the quantum fluctuations of the seed and pump waves. Unlike the preceding theoretical studies of the problem, we show that squeezing in bright beams produced by the OPO depends on their intensity. For the amplitude-squeezed state, squeezing strongly degrades with increasing output intensity. In contrast, one can obtain good squeezing for phase-squeezed beams of high output intensity.