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European Quantum Electronics Conference (EQEC)

Quantum Imagess in Non Degenerate Optical Parametric Oscillators

C. Szwaj, Gian‐Luca Oppo

Published Aug 24, 2005• 0 citations
Publisher

Abstract

Quantum images, that is inhomogeneous field distributions purely generated by quantum fluctuations, persist when passing from the degenerate to the non-degenerate case of optical parametric oscillators (OPO). Below the threshold for parametric oscillation where the near-field distributions are homogeneous both in intensity and phase, appropriate spatial correlation functions anticipate the transverse spatial pattern that appears above threshold. In particular, the angular dependence of the far field spatial correlation function is able to reveal the travelling-wave nature of the phase pattern above threshold typical of nondegenerate OPOs. Cross-correlation functions between signal and idler intensities show clear evidence of the non-classical nature of the output light.

DOI
10.1109/eqec.1998.715167

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Quantum images, that is inhomogeneous field distributions purely generated by quantum fluctuations, persist when passing from the degenerate to the non-degenerate case of optical parametric oscillators (OPO). Below the threshold for parametric oscillation where the near-field distributions are homogeneous both in intensity and phase, appropriate spatial correlation functions anticipate the transverse spatial pattern that appears above threshold. In particular, the angular dependence of the far field spatial correlation function is able to reveal the travelling-wave nature of the phase pattern above threshold typical of nondegenerate OPOs. Cross-correlation functions between signal and idler intensities show clear evidence of the non-classical nature of the output light.
A Langevin model is introduced to study quantum fluctuations below the threshold of pattern formation for optical parametric oscillators (OPO's). In particular we compare analytical and numerical results for the OPO with one and two transverse spatial dimensions and in the presence of either plane or spherical cavity mirrors. The far-field structure and the correlation functions of the fluctuating signal field anticipate the onset of a transverse spatial pattern which arises classically even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field. Numerical simulations of the Langevin model describe the result of short time measurements and show that close to threshold the near-field signal is a noisy spot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experimentally accessible.
We illustrate the spatial quantum features that emerge in a degenerate optical parametric oscillator below threshold, where the signal field is purely generated by quantum fluctuations. We analyze the behaviour of the spatial correlation function of a generic quadrature component of the signal field in both cases of a cavity with plane mirrors and a cavity with spherical mirrors. The correlation length diverges when the semiclassical threshold for signal field generation is approached. We focus on the novel concept of quantum image, which is analyzed both in the near field and in the far field.
In the first part of the paper we define the spatial spectrum of squeezing following an operational procedure, and we show in general how the spatial structure of squeezed states can be described in terms of correlation functions of quadrature components of the electric field. In the second part we formulate an appropriate quantum model for a degenerate optical parametric oscillator (OPO) with plane mirrors, and we analyze it extensively below the threshold for signal generation. The correlation length diverges when the OPO approaches threshold; this picture provides an ideal completion of the analogy with critical phenomena in second-order phase transition at equilibrium. The spatial configuration of the correlation function exhibits the phenomenon of ``quantum image:'' the signal field, which is purely generated by quantum noise, shows an ordered spatial structure which is observable via the spatial correlation function.
Fluctuations in the field of a 2nd order nonlinear multi-mode parametric downcoverter exhibit nonclassical correlations in the transverse plane. We present results of measurements of the classical pattern for a degenerate, multi-mode parametric optical parametric oscillator (OPO) operating above threshold. We also present results of autocorrelation measurements of intensity fluctuations in the transverse plane both in the near field and in the far field with the OPO operating both below and above threshold -- a method we believe will ultimately enable us to display the nonclassical correlations of the OPO output.
We illustrate the concept of quantum image in the context of degenerate parametric oscillators. In the case of a cavity with planar mirrors, we show the gradual transformation of a quantum image into a classical image as the threshold region is scanned. Thus the quantum image behaves as a precursor of the roll pattern which appears above threshold. In the far field, the configuration of the spatial correlation function of the intensity and of the quadrature components shows unambiguously the quantum nature of fluctuations that generate the quantum image, leading to effects of quantum noise reduction below the shot noise level, and to the formulation of an Einstein–Podolsky–Rosen paradox.
Summary form only given.We study spatiotemporal fluctuations of the signal field in the output from a degenerate optical parametric oscillator using the Langevin model of A. Gatti et al. (1997). The spatial structure of the output signal is calculated for pump values just below the threshold for the formation of patterns with a critical wave vector. We consider the effects of a squeezed input signal, both homogeneous and spatially varying, on the output correlations, which can be measured in both the near- and far-field.