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arXiv:quant-ph/0604002 · Optics Express

3D phase-matching conditions for the generation of entangled triplets by χ^(2) interlinked interactions

Maria Bondani, Alessia Allevi, Eleonora Gevinti, Andrea Agliati, Alessandra Andreoni

Published Oct 16, 2006• 15 citations
arXivHTMLPDF

Abstract

An analytical calculation of the interaction geometry of two interlinked second-order nonlinear processes fulfilling phase-matching conditions is presented. The method is developed for type-I uniaxial crystals and gives the positions on a screen beyond the crystal of the entangled triplets generated by the interactions. The analytical results are compared to experiments realized in the macroscopic regime. Preliminary tests to identify the triplets are also performed based on ntensity correlations.

DOI
10.1364/oe.14.009838

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An analytical calculation of the interaction geometry of two interlinked second-order nonlinear processes fulfilling phase-matching conditions is presented. The method is developed for type-I uniaxial crystals and gives the positions on a screen beyond the crystal of the entangled triplets generated by the interactions. The analytical results are compared to experiments realized in the macroscopic regime. Preliminary tests to identify the triplets are also performed based on ntensity correlations.
The geometrical conditions are analytically calculated in which two interlinked second-order nonlinear interactions generating entangled triplets are phase-matched in 3D. The interactions are the spontaneous parametric downconversion of an intense pump and the upconversion of a portion of the downconversion cones by a further pump. The calculation applies to type-I interactions occurring in uniaxial crystals and allows us to forecast positions and frequencies of the entangled triplets experimentally generated. The photon number statistics and the intensity correlations are also measured.
We address the generation of fully inseparable three-mode entangled states of radiation by interlinked nonlinear interactions in χ(2) media. We show how three-mode entanglement can be used to realize symmetric and asymmetric telecloning machines, which achieve optimal fidelity for coherent states. An experimental implementation involving a single nonlinear crystal in which the two interactions take place simultaneously is suggested. Preliminary experimental results showing the feasibility and the effectiveness of the interaction scheme with a seeded crystal are also presented.
The transcendental equations of vector phase matching are transformed into a fourth-order polynomial equation that admits an analytical solution. The real roots of this equation provide the optical axis orientations that are useful for efficient down-conversion in nonlinear uniaxial crystals. The production of entangled photon pairs is discussed in both collinear and non-collinear configurations of the spontaneous parametric down-conversion (SPDC) process. Degenerate and non-degenerate cases are also distinguished. As a practical example, SPDC processes of type-I and type-II are studied for beta-barium borate (BBO) crystals. The predictions are in very good agreement with experimental measurements already reported in the literature and include theoretical results of other authors as particular cases. Some properties that seem to be exclusive to BBO crystals are reported; the experimental verification of the latter would allow a better characterization of these crystals.
Two-photon entangled generation is used to produce an entangled photon source which is a key and core element concerning the technology applications of quantum computing, quantum communication, and quantum precision measurement. In this work, we have deduced the formulas of dynamic susceptibility and phase-matching angle of two-photon entangled generation in nonlinear optical crystals. The formulas are employed to compute the susceptibilities and phase-matching angles of these optical processes for uniaxial and biaxial crystals. The susceptibility magnitude and phase-matching condition of two-photon entangled generation affect the performance of the source. The calculated results by these formulas are employed to study properties and estimate the performance of an entangled photon source. In this way, we discuss the phase matching among waves and working wavelength in an entangled source that affects the efficiency of satellite communication with the ground during the day and night.