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arXiv:quant-ph/0306134 · Physical Review A

Polarization quantum properties in a type-II optical parametric oscillator below threshold

Roberta Zambrini, A. Gatti, Luigi Lugiato, Maxi San Miguel

Published Dec 10, 2003• 10 citations
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Abstract

We study the far-field spatial distribution of the quantum fluctuations in the transverse profile of the output light beam generated by a type-II optical parametric oscillator below threshold, including the effects of transverse walk-off. We study how quadrature field correlations depend on the polarization. We find spatial Einstein-Podolsky-Rosen entanglement in quadrature-polarization components. For the far-field points not affected by walk-off there is almost complete noise suppression in the proper quadratures difference of any orthogonal polarization components. We show the entanglement of the state of symmetric, intense, or macroscopic, spatial light modes. We also investigate nonclassical polarization properties in terms of the Stokes operators. We find perfect correlations in all Stokes parameters measured in opposite far-field points in the direction orthogonal to the walk-off, while locally the field is unpolarized and we find no polarization squeezing.

DOI
10.1103/physreva.68.063809

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We study the far-field spatial distribution of the quantum fluctuations in the transverse profile of the output light beam generated by a type-II optical parametric oscillator below threshold, including the effects of transverse walk-off. We study how quadrature field correlations depend on the polarization. We find spatial Einstein-Podolsky-Rosen entanglement in quadrature-polarization components. For the far-field points not affected by walk-off there is almost complete noise suppression in the proper quadratures difference of any orthogonal polarization components. We show the entanglement of the state of symmetric, intense, or macroscopic, spatial light modes. We also investigate nonclassical polarization properties in terms of the Stokes operators. We find perfect correlations in all Stokes parameters measured in opposite far-field points in the direction orthogonal to the walk-off, while locally the field is unpolarized and we find no polarization squeezing.
The paper reports on the investigation on to which extent the microscopic polarization properties survive at a macroscopic level, in presence of a continuous flux of photons, in a transverse spatially extended system. A prototype device to generate polarization entangled beams is a quadratic crystal in the type II phase matching configuration. The spectral brightness can be increased by means of a resonant cavity (optical parametric oscillator) . Quantum correlations below threshold is calculated analytically taking into account the walk-off effect between the (ordinary polarized) signal and the (extraordinary polarized) idler. In this regime the average of the signal field is zero, but the far-field (FF) intensity distribution is dominated by two undamped rings (quantum images, noisy precursors of the pattern), whose centers are displaced along the walk-off direction. In the first part, the effect of the selection of different polarization components on the Einstein-Podolsky-Rosen correlations is studied; this is a generalization of the first experimental realization of the EPR paradox for continuous variables in an OPO, taking now into account the transverse profile of the filed. In the second part, the correlations in other continuous variables, the Stokes parameters are then analyzed.
We study theoretically and experimentally the quantum properties of a type-II frequency-degenerate optical parametric oscillator below threshold with a quarter-wave plate inserted inside the cavity which induces a linear coupling between the orthogonally polarized signal and idler fields. This original device provides a good insight into general properties of two-mode Gaussian states, illustrated in terms of the covariance matrix. We report on the experimental generation of a two-mode squeezed vacuum on nonorthogonal quadratures depending on the plate angle. After a simple operation, the entanglement is maximized and put into standard form, i.e., quantum correlations and anticorrelations on orthogonal quadratures. A half sum of squeezed variances as low as $0.33\ifmmode\pm\else\textpm\fi{}0.02$, well below the unit limit for inseparability, is obtained and the entanglement measured by the entropy of formation.
SUMMARY Parametric processes in the interaction of electromagnetic field with a medium in an optical cavity are well known to produce states of light with nonclassical properties. The quantum correlations between these states can be employed for a realization of an EinsteinPodolsky-Rosen (EPR) paradox [l], in the original formulation using continuous variables, as proposed [2] and experimentally demonstrated [3] in the case of Nondegenerate Parametric Amplification below threshold. In this paper we study EPR-like behaviour between the signal and idler fields emitted by a degenerate optical parametric oscillator (OPO) above threshold; these fields, generated by conversion of a pump photon of frequency 2w0 in two photons of frequency w. , are spatially separated in the far field, showing non-local quantum correlations. The system is described by the full Hamiltonian for the operators associated with the pump and signal fields; the optical cavity introduces proper damping constants and corresponding vacuum field operators [4,5]. Above the threshold for the generation of the signal field, we consider the fluctuations in the intensity difference and in the phase sum of the signal beams, which are related to their degree of mutual correlation. By linearizing around the stationary state, we calculate the spectral variances of these quantities (i.e. the Fourier transform of the two time correlation functions). The Heisenberg uncertainty principle sets a lower limit to the product of the spectral variances for the fluctuations in the intensity and in the phase of each individual signal field; by using the idler beam to infer results of measurements on the correlated signal beam, we have an EPR paradox if the product of the spectral variances for the fluctuations in the intensity difference and phase sum of the fields, is below the uncertainty limit. This feature is apparent for a wide interval around zero frequency in the far field of the active OPO system, depending on the parameter space; in particular there is maximum correlation between signal beams, and therefore maximum breaking of the uncertainty limit, if the damping constant of the signal field is larger than that of the pump field.
The effects of an intracavity photonic crystal in a multimode optical parametric oscillator are studied, with a special focus on quantum fluctuations. The capability to either stimulate or inhibit the spatial instability, lowering or increasing the parametric threshold, allows to control the intensity fluctuations and correlations. A significative quantum noise reduction and an increase of the range of squeezed quadratures are found above threshold where spatial Einstein-Podolsky-Rosen entanglement and inseparability are found.
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.