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Physical Review A

Possibility of efficient generation of multiphoton entangled states using a one-dimensional nonlinear photonic crystal

Yunxia Dong, Xiangdong Zhang

Published Mar 8, 2010• 4 citations
Publisher

Abstract

A rigorous quantum theory for the generation of multiphoton entangled states based on two consecutive three-frequency interactions of waves in a one-dimensional nonlinear photonic crystal is developed using the field expansion and differentiation methods. The three-photon correlation coefficient and the average photon numbers generated in the structure are calculated. All order expansion terms are included in the calculation. The generation conditions for multiphoton entangled states in such a structure are also analyzed. It is shown that the created photons in the present structures obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state. This means the nonlinear photonic crystal can be applied as a highly efficient source of an entangled multiphoton for highly integrated all-optical circuits.

DOI
10.1103/physreva.81.033806

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A rigorous quantum theory for the generation of multiphoton entangled states based on two consecutive three-frequency interactions of waves in a one-dimensional nonlinear photonic crystal is developed using the field expansion and differentiation methods. The three-photon correlation coefficient and the average photon numbers generated in the structure are calculated. All order expansion terms are included in the calculation. The generation conditions for multiphoton entangled states in such a structure are also analyzed. It is shown that the created photons in the present structures obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state. This means the nonlinear photonic crystal can be applied as a highly efficient source of an entangled multiphoton for highly integrated all-optical circuits.
Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.
Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic Al0.4Ga0.6As/air structure for the generation of 1.5 microm light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.
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.
We propose a two-dimensional ${\ensuremath{\chi}}^{(2)}$ nonlinear photonic crystal capable of satisfying quasi-phase-matching conditions for two or three parametric down-conversions simultaneously. Seeded by a two-mode coherent state, this crystal can produce two-, three-, four-, or five-photon path-entangled states, provided the corresponding number photons are produced, i.e., in a postselection-free way. In particular, up to five-photon NOON state can be generated, which enables phase supersensitive measurements at the Heisenberg limit. The concurrent multiple quasi-phase-matchings provided by the nonlinear photonic crystal open up a way to integrated quantum light sources.
We propose a compact scheme for the heralded generation of single-photon multipartite entanglement by using a single two-dimensional nonlinear photonic crystal. Studies have shown that by appropriate structure design, the single-photon entanglement shared among three spatially distinct optical modes can be generated through three concurrent spontaneous parametric down-conversion processes by using the other photon in an identical spatial mode as a trigger. Furthermore, we analyze the entanglement of such heralded single-photon tripartite W-type state theoretically. This method can be expanded for the heralded single-photon N-partite entanglement generation. This compact and stable quantum light source may act as a key ingredient in quantum information science.
Multipartite quantum entanglement is a powerful resource for enriching the functionality of quantum computation and quantum communication. In this Letter, we propose a new method to generate a two-photon multipath Dicke state with concurrent spontaneous parametric downconversion processes from a single periodically poled nonlinear photonic crystal. We design the poling structure to produce a three-path Dicke state where three quasi-phase-matching conditions are fulfilled simultaneously by a hybrid one- and two-dimensionally poled nonlinear photonic crystal. We use genuine multipartite entanglement concurrence to quantify the entanglement of the Dicke state. Using a more complicated poling configuration like multiple-periodically poled two-dimensional nonlinear photonic crystal, we can also produce four-path, five-path, or multipath Dicke states by a single crystal. The multiple-periodically poled two-dimensional nonlinear photonic crystal provides a new method, to the best of our knowledge, for the integrated generation of multipartite quantum light sources.