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Quantum Optics Journal of the European Optical Society Part B

Quantum noise reduction in the squeezed pump non-degenerate parametric oscillator

William J. Munro, M. D. Reid

Published Jun 1, 1992• 6 citations
Publisher

Abstract

The authors present a simple quantum model of the non-degenerate parametric oscillator above threshold where the pump has squeezed fluctuations. Quantum noise reduction is predicted not only for the signal and idler beams intensity difference, but also for the intensity sum. For pumps with greatly reduced intensity fluctuations, near perfect squeezing is also predicted for the individual signal and idler intensities.

DOI
10.1088/0954-8998/4/3/006

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The authors present a simple quantum model of the non-degenerate parametric oscillator above threshold where the pump has squeezed fluctuations. Quantum noise reduction is predicted not only for the signal and idler beams intensity difference, but also for the intensity sum. For pumps with greatly reduced intensity fluctuations, near perfect squeezing is also predicted for the individual signal and idler intensities.
A quantum analysis of the above-threshold intensity fluctuations in a nondegenerate parametric oscillator with direct-detection feedback onto the pump amplitude is presented. We derive a master equation for the signal (in-loop) and idler (out-of-loop) modes by adiabatically eliminating the pump mode and incorporating a feedback term, using the Wiseman-Milburn quantum feedback theroy [Phys. Rev. Lett. 70, 548 (1993)]. In the absence of feedback and far above threshold, we find that both beams are 50% intensity squeezed. For small negative (positive) feedback, the intensity fluctuations in the out-of-loop (in-loop) beam are reduced further. For larger values of feedback, the fluctuations grow, the fields eventually becoming unsqueezed.
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.
A semi-classical analysis of the noise characteristics of a non degenerate, above threshold, optical parametric oscillator is presented, yielding expressions for the quantum fluctuations of the output field intensities and phases. Particular emphasis is given to the study of the noise on the intensity difference between the two generated fields. The effect of losses, unbalance, detunings and excess pump noise is investigated. A significant quantum noise reduction is found over a broad domain of the parameter space.
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.