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Conference on Lasers and Electro-Optics

“Backward Heisenberg picture” approach for spontaneous parametric down-conversion

Zhenshan S. Yang, Marco Liscidini, John E. Sipe

Published May 1, 2008• 0 citations
Publisher

Abstract

We develop a fully quantum-mechanical approach for describing spontaneous parametric down-conversion, which allows us to write an expression for the quantum state easily, even when multiple photon pairs are generated in the process.
DOI
10.1109/cleo.2008.4552134

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We develop a fully quantum-mechanical approach for the description of spontaneous parametric down-conversion in waveguides. Our method allows us to write an expression for the quantum state easily and directly, even when multiple photon pairs are generated in the process. The role of material dispersion in the normalization of the modes of the system, usually neglected, is properly treated here. The example of an AlyOx/Al0.5Ga0.5As{\text{Al}}_{y}{\text{O}}_{x}/{\text{Al}}_{0.5}{\text{Ga}}_{0.5}\text{As}Aly​Ox​/Al0.5​Ga0.5​As ridge waveguide is discussed to illustrate the application of the formalism.
An effective-medium approach is used to derive a set of coupled-mode equations describing quadratic parametric interactions in a one-dimensional inhomogeneous medium of finite length. The solutions for both copropagating and counterpropagating interactions are used to study the quantum-mechanical process of spontaneous parametric down-conversion (SPDC). An example is studied in which the inhomogeneous medium is a photonic crystal. The effect that device geometry has on both the efficiency and bandwidth of SPDC is explored. With appropriate design, we find that it is possible not only to enhance the efficiency of SPDC, but also to generate broadband copropagating and narrowband counterpropagating down-converted light. A setup is proposed with the potential to act as a source of entangled photon pairs.
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.