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Conference on Lasers and Electro-Optics

Quantum correlations in noise-sustained optical patterns

Stephen Mark Barnett, Roberta Zambrini, Gonzalo G. Izús, Maxi San Miguel, Pere Colet

Published Aug 29, 2005• 1 citation
Publisher

Abstract

Summary form only given. Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective regime of a degenerate type-I optical parametric oscillator (OPO) using a time dependent parametric approximation, in which the intracavity pump field is taken as a classical stochastic field.

DOI
10.1109/iqec.2000.907770

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Summary form only given. Noise-sustained patterns have been recently predicted in several systems including a Kerr cavity and an optical parametric oscillator. In these systems a regime of convective instability can appear, in which a transverse pattern arises as a macroscopic manifestation of amplified and spatially structured quantum noise, with magnification factors of several order of magnitudes. We study quantum correlations in the convective regime of a degenerate type-I optical parametric oscillator (OPO) using a time dependent parametric approximation, in which the intracavity pump field is taken as a classical stochastic field.
We investigate quantum effects in pattern formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based on linearization about a pseudoclassical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a c-number variable but is driven by the c-number representation of the quantum subharmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the nonclassical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further, above threshold, the macroscopic quantum noise suppresses these effects.
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 theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive PPP representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.
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.
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.