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Physical Review A

Generation of positively-momentum-correlated biphotons from spontaneous parametric down-conversion

Sujun Yun, Ping Xu, J. S. Zhao, Yan-Xiao Gong, Y. F. Bai, J. Shi, Shining N. Zhu

Published Aug 29, 2012• 14 citations

Abstract

We propose to generate a counter-Einstein-Podolsky-Rosen (CEPR) state which possesses a positively-correlated momentum and anticorrelated position directly from spontaneous parametric down-conversion. The general CEPR state is given under a tightly focused Gaussian pump based on type II noncritical phase matching. We analytically and numerically study how a positively-correlated momentum and anticorrelated position of a biphoton can be achieved by choosing the proper focal parameter of the pump. To verify the degree of entanglement of the CEPR state, we calculate its entanglement entropy and it shows a unique dependence on the pump's focal parameter. Suggestions for practical engineering of the state are also given. Furthermore, based on an ideal CEPR state, we deduce a type of erect quantum ghost imaging which can be applied as the entanglement criterion. This work gives applicable references to the spatial control of an entangled photon source in experiments and may stimulate the development of new types of quantum technologies.

DOI: 10.1103/physreva.86.023852

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The most common source of entangled photons is spontaneous parametric down-conversion (SPDC). The degree of energy and momentum entanglement in SPDC is determined by the nonlinear interaction volume. By reducing the length of a highly nonlinear material, we relax the longitudinal phase-matching condition and reach record levels of transverse momentum entanglement. The degree of entanglement is estimated using both correlation measurements and stimulated emission tomography in wave-vector space. The high entanglement of the state in wave-vector space can be used to massively increase the quantum information capacity of photons, but more interestingly the equivalent state measured in position space is correlated over distances far less than the photon wavelength. This property promises to improve the resolution of many quantum imaging techniques beyond the current state of the art.

Coherence is a fundamental property of light. Recent years have witnessed a growing interest in coherence structuring, yielding a new type of partially coherent source with spatially tailored nonuniform correlations. However, the routine way of producing entangled photons via parametric down-conversion is to use a highly coherent laser source to pump nonlinear crystals. Here, we present a new strategy of exploiting such nonuniformly partially coherent sources to excite parametric down-conversion and thus endow the generated entanglement with a tailored and unusual spatial symmetry. To reveal the spatially varying degree of entanglement, we demonstrate the observation of an unusual Einstein-Podolsky-Rosen (EPR) correlation by transferring the circular structure of the coherence of the pump beam onto that of down-converted photons. For this, we observe both anomalous ghost diffraction and normal ghost images to examine the EPR-type inequalities and showcase the transition from nonentanglement to entanglement. Our work suggests that coherence structuring can offer a new dimension to generate and control quantum entanglement.

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