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Optics Letters

Properties of two interlinked χ^(2) interactions in noncollinear phase matching

Maria Bondani, Alessia Allevi, Emiliano Puddu, Alessandra Andreoni, Alessandro Ferraro, Matteo G. A. Paris

Published Jan 15, 2004• 48 citations
Publisher

Abstract

We present a compact experimental realization of the interaction among five field modes in a chi(2) nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal.

DOI
10.1364/ol.29.000180

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We present a compact experimental realization of the interaction among five field modes in a chi(2) nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal.
Three-wave interactions occurring in conditions of type I phase matching in a uniaxial crystal are considered in the general case of noncollinear wave propagation. It is demonstrated that, if one among the interacting fields at ${\ensuremath{\omega}}_{i}(i=1,2,3)$ is virtually unaffected in amplitude by the interaction, the remaining two fields at ${\ensuremath{\omega}}_{j}(j\ensuremath{\ne}i)$ are holographic replicas of each other, the constant field acting as the reference field in holography. Experiments are presented in which a holographic image of an object consisting in a pointlike light source is obtained by either up- or down-conversion for any choice of the object- and reference-field frequencies among ${\ensuremath{\omega}}_{1},$ ${\ensuremath{\omega}}_{2},$ and ${\ensuremath{\omega}}_{3}.$
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.
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.
We consider two interlinked non-linear interactions occurring simultaneously in a single x(2) crystal. Classical and quantum working regimes are considered and their peculiar properties analysed. In particular, we describe an experiment, realized in the classical regime, that verifies the holographic nature of the process, and predict, for the quantum regime, the generation of a fully inseparable tripartite Gaussian state of light that can be used to support a general 1 →2 continuous variable telecloning protocol.
We examine the tripartite entanglement properties of an optical system using interlinked ${\ensuremath{\chi}}^{(2)}$ interactions, recently studied experimentally in terms of its phase-matching properties by Bondani et al. [Opt. Express 14, 21, 9838 (2006)]. We show that the system produces output modes at three distinct frequencies which are genuinely tripartite entangled, and analyze this entanglement in terms of different measurable correlations. We show that, due to the asymmetry of the process, the detection of this entanglement depends crucially on the correlation functions that are measured. We find that some of the correlations found in the literature fail to register the entanglement, in contrast to symmetric systems, for which the actual choice of correlation to be measured makes little difference.