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arXiv:quant-ph/0604017 · Physical Review A

Properties of entangled photon pairs generated in one-dimensional nonlinear photonic-band-gap structures

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

Published Mar 30, 2006• 35 citations
arXivHTMLPDF

Abstract

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 $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ is analyzed as a suitable source of photon pairs having high efficiency.

DOI
10.1103/physreva.73.033823

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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.
Nonlinear metal-dielectric layered structures are shown to be able to efficiently generate entangled photon pairs using spontaneous parametric down-conversion. Increase of electric-field amplitudes in these structures enhanced by the presence of metal layers is sufficient to compensate for losses inside thin metal layers. As an example, photon pairs emitted from a structure composed of alternating nonlinear dielectric GaN layers and metal Ag layers are analyzed in spectral, temporal, as well as spatial domains. Also, correlations and entanglement between two photons in a pair are determined. Very narrow photon-pair spectra together with strong directionality of photon-pair emission are observed making the photons suitable for photon-atom interactions. Highly enhanced electric-field amplitudes provide high photon-pair generation efficiencies.
We describe properties of entangled photon pairs generated by spontaneous parametric down-conversion in periodically poled nonlinear crystals. These materials can serve as a useful bright source of photon pairs which properties can be tailored on demand. Especially photon pairs with broad spectra and sharp temporal features can be observed. Both uniform and chirped poling are considered. Spectral properties of the generated photons, photon fluxes, coincidence-count patterns in a Hong-Ou-Mandel interferometer, entropy of entanglement, as well as transverse profiles of intensities of the generated photon fields are discussed. Also the correlation area of two photons comprising a photon pair has been studied as it depends on parameters of periodical poling. Attention is also paid to structures with randomly distributed boundaries.
A nonlinear planar waveguide pumped by a beam orthogonal to its surface may serve as a versatile source of photon pairs. By changing the pump-pulse duration, pump-beam transverse width, and angular decomposition of the pump-beam frequency characteristics of a photon pair, including the spectral widths of signal and idler fields, the pair time duration as well as the degree of entanglement of the two fields, can be changed significantly. Using the measured spectral widths of the down-converted fields and the width of a coincidence-count dip in a Hong-Ou-Mandel interferometer, the entropy of entanglement can be determined.
We demonstrate a general method of engineering the joint quantum state of photon pairs produced in spontaneous parametric down-conversion. The method makes use of a superlattice structure of nonlinear and linear materials, in conjunction with a broadband pump, to manipulate the group delays of the signal and idler photons relative to the pump pulse, and realizes photon pairs described by a joint spectral amplitude with arbitrary degree of entanglement. This method of group-delay engineering has the potential of synthesizing a broad range of states including factorizable states crucial for quantum networking and states optimized for Hong-Ou-Mandel interferometry. Experimental results for the latter case are presented, illustrating the principles of this approach.