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International Conference on Transparent Optical Networks

Nonlinear Photonic-Band-Gap Structures Made of GaN/AlN as a Source of Entangled Two-Photon States

Jan Peřina, Marco Centini, Concita Sibilia, M. Bertolotti, Michael Scalora

Published Jun 1, 2006• 1 citation
Publisher

Abstract

We have developed a vectorial quantum model of spontaneous parametric down-conversion in one-dimensional nonlinear photonic-band-gap structures. According to the obtained results these structures represent a promising perspective source of entangled two-photon states. In particular, entangled two-photon states antisymmetric in frequencies can be generated. Such entangled photons behave in the way resembling two fermions

DOI
10.1109/icton.2006.248316

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Physical Review A•Sep 9, 2005•31 citations
We have developed a vectorial quantum model of spontaneous parametric down-conversion in one-dimensional nonlinear photonic-band-gap structures. According to the obtained results these structures represent a promising perspective source of entangled two-photon states. In particular, entangled two-photon states antisymmetric in frequencies can be generated. Such entangled photons behave in the way resembling two fermions
The properties of an entangled two-photon state antisymmetric in frequencies are studied. At a beam splitter, two entangled photons are perfectly anticorrelated. In addition, they cannot be detected at the same time instant despite the fact that their detection times are confined to a narrow time window, i.e., they are temporally antibunched. Using nonlinear photonic-band-gap structures made of GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN, two schemes for generating such states are described.
We have developed a rigorous quantum model of spontaneous parametric down-conversion in a nonlinear 1D photonic-band-gap structure based upon expansion of the field into monochromatic plane waves. The model provides a two-photon amplitude of a created photon pair. The spectra of the signal and idler fields, their intensity profiles in the time domain, as well as the coincidence-count interference pattern in a Hong-Ou-Mandel interferometer are determined both for cw and pulsed pumping regimes in terms of the two-photon amplitude. A broad range of parameters characterizing the emitted down-converted fields can be used. As an example, a structure composed of 49 layers of GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN is analyzed as a suitable source of photon pairs having high efficiency.
A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also, structures efficiently generated photon pairs showing antibunching and anticoalescence can be obtained. Three reasons for splitting the correlated area in photonic-band-gap structures are revealed: zig-zag movement of photons inside the structure, spatial symmetry, and polarization-dependent properties. Also, spectral splitting can be observed in these structures.
A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN∕AlN\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}GaN∕AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.