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Physical Review A

Noise reduction in the nondegenerate parametric oscillator with direct detection feedback

John J. Slosser, Gerard J Milburn

Published Jul 1, 1994• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.793

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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.
Noise spectra of the in-phase and quadrature-phase components of the signal and idler fields of a nondegenerate optical parametric amplifier are calculated. It is shown that, as is suggested by the operator Manley-Rowe relations, the external in-phase (amplitude) fluctuations of the signal and idler fields are correlated in the frequency region lower than the signal and idler cavity bandwidths. If the idler photon flux is continuously measured and the photocurrent fluctuations are fed back to control the pump intensity, the signal output will feature an amplitude noise spectral density reduced to below the standard quantum limit (amplitude squeezing) in the frequency region below the feedback loop and signal and idler cavity bandwidths. An all-optical realization of such a negative-feedback parametric oscillator is presented. It is also shown that a nondegenerate parametric amplifier with idler measurement feedback can add a fixed number of photons to a photon-number state.
The phase-fluctuation correlation between the signal and idler fields in nondegenerate parametric optical amplifiers and oscillators is analyzed. It is shown that close to the threshold pump power, the correlation is sufficient to reduce the phase fluctuations below those of a coherent state. The phase-fluctuation correlation is negative due to the simultaneous phase matching and energy conservation. This restricts the usefulness of the correlation. The pump source's phase noise will furthermore set a limit to the minimum achievable phase spectral density. The conditions for surpassing the standard quantum limit are elaborated. Finally, applications to coherent optical communication and gravitational wave detection are discussed.
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.
It has been recently shown theoretically1 and experimentally2 that nondegenerate optical parametric oscillators generate above threshold intense and highly correlated twin beams. More precisely, the noise on the difference between the intensities of the two beams is well below the shot noise for noise frequencies inside the cavity bandwidth. An application of this quantum correlation is to measure the intensity of one beam and use this information to correct the fluctuations of the other beam by optoelectronic means (photodiode, amplifier, and electrooptic modulator). The correction may be applied either on the pumping beam (feedback correction) or directly on the twin beam itself (feed-forward correction).