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Frontiers in Optics

Observation of different types of spatial correlations in the biphoton’s Fourier plane

Omar Calderón-Losada, Jefferson Flórez, Juan P. Villabona-Monsalve, Alejandra Valencia

Published Jan 1, 2015• 0 citations
Publisher

Abstract

We report an experiment based on non-collinear type-II spontaneous parametric down-conversion that shows how the type of spatial correlation changes if the biphoton’s Fourier plane is scanned vertically or horizontally.
DOI
10.1364/fio.2015.fw3a.6

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We show that the wave packet of a biphoton generated via spontaneous parametric down-conversion is strongly anisotropic. Its anisotropic features manifest themselves very clearly in comparison with measurements performed in two different schemes: When the detector scanning plane is perpendicular or parallel to the plane containing the crystal optical axis and the laser axis. The first of these two schemes is traditional whereas the second one gives rise to such unexpected results, such as anomalously strong narrowing of the biphoton wave packet measured in the coincidence scheme and very high degree of entanglement. The results are predicted theoretically and confirmed experimentally.
Correlations in light can be used for a variety of applications in metrology and imaging. Several schemes in quantum imaging rely on multi-photon absorption. Therefore a detailed knowledge of the temporal and spatial correlations of the photons used is desired. This paper investigates the correlations of space-momentum entangled biphotons generated from type II parametric down conversion. The type II generation allows for individual manipulation in each path to control the spatial modes involved in the subsequent biphoton beam creation utilizing a Hong-Ou-Mandel interference.
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Abstract As a tutorial to the spatial aspects of spontaneous parametric downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we show how this biphoton amplitude can be approximated with a double-Gaussian wavefunction, and give a brief discussion of the measurement statistics (and subsequent convenience) of such double-Gaussian wavefunctions. Next, we use this approximation to get a simplified estimation of the transverse correlation width, and compare it to more accurate calculations as well as experimental results. We then conclude with a discussion of the concept of a biphoton birth zone, using it to develop intuition for the tradeoff between the first-order spatial coherence and bipohoton correlations in SPDC.