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Photon Correlation and Scattering

Photon correlations in type-I optical parametric down-conversion

Edward R. Pike, Sarben Sarkar, Roger Andrews

Published Jan 1, 2000• 0 citations
Publisher

Abstract

We develop a quantum theory for photon-pair correlations in Type-1 spontaneous parametric down-conversion, including crystal dispersion. We obtain different amplitudes for the correlations of degenerate (identical frequencies) and non-degenerate (different frequencies) signal and idler photons.
DOI
10.1364/pcs.2000.md3

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In this work we develop a quantum theory for fourth-order interference effects of non-degenerate (ND) and degenerate (D) photons produced in type-I spontaneous parametric down-conversion. In the first part of this work we include the effect of crystal dispersion whereby we obtain distinct amplitudes for ND and D photons. In the second part, the effects produced by changes in crystal length and beam-waist radius on photon-pair correlations and fourth-order interference were examined. The effect of such changes on ND and D photons was found to be different and therefore we conclude that ND and D photons are inherently distinguishable quantum states of the photon field.
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A theory is presented for the quantum state of photon pairs generated from spontaneous parametric down-conversion nonlinear process. In this theory, the influence of the final sizes of nonlinear optical crystals on optical eigenmodes is explicitly taken into consideration. It was found that these photon pairs are not in entangled quantum states. Polarization correlations between the signal beam and the idler beam are explained. It is also shown that the two photons generated from SPDC are not spatially separated, therefore the polarization correlation between the signal and idler beams is not an evidence for quantum non-locality.
A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter