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Journal of the Optical Society of America B

Triple-photon generation: comparison between theory and experiment

Fabien Gravier, Benoı̂t Boulanger

Published Dec 21, 2007• 28 citations
Publisher

Abstract

We conceived an optical generator leading to the production of 3×1013 triple photons per pulse with a full-width duration of 88ps at 1/e2, by using a third-order optical parametric interaction phase-matched in a KTP crystal and pumped at 532 nm. The triple photon generation is stimulated by two photons orthogonally polarized emitted by a homemade optical parametric oscillator emitting at 1665 nm. The energy generated at 1474 nm is well modelized by an analytical model based on Jacobi elliptic functions. These results open the way to new quantum measurement relative to Greenberger-Horne-Zeilinger state of light.

DOI
10.1364/josab.25.000098

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We conceived an optical generator leading to the production of 3×1013 triple photons per pulse with a full-width duration of 88ps at 1/e2, by using a third-order optical parametric interaction phase-matched in a KTP crystal and pumped at 532 nm. The triple photon generation is stimulated by two photons orthogonally polarized emitted by a homemade optical parametric oscillator emitting at 1665 nm. The energy generated at 1474 nm is well modelized by an analytical model based on Jacobi elliptic functions. These results open the way to new quantum measurement relative to Greenberger-Horne-Zeilinger state of light.
Triple Photon Generation (TPG) is a third-order nonlinear optical interaction in which a photon of energy ℏωp splits into three photons at ℏω1, ℏω2, and ℏω3, with ℏωp = ℏω1 + ℏω2 + ℏω3. The triplets possess different quantum signatures from those of photon pairs, with strong interest in quantum information. In the present study, we report the first experimental demonstration of TPG stimulated over one mode of the triplet, at ℏω1, whereas previous work on TPG concerned stimulation over two modes, at ℏω2 and ℏxω3. The nonlinear medium is a KTiOPO4 crystal pumped in the picosecond regime (15 ps, 10 Hz) at λp = 532 nm. The stimulation beam is emitted by a tunable optical parametric generator: the phase-matching was found at a stimulation wavelength λ1 = 1491 nm, the other two modes of the triplet being at λ2 = λ3 = 1654 nm in orthogonal polarizations. Using superconducting nanowire single photon detectors, the measurements of the polarizations and wavelength signatures of the two generated modes are in full agreement with calculations. It has been possible to generate a total number of photons per pulse on modes 2 and 3 up to 2 × 104, which corresponds to the generation of 104 triplets per pulse, or 105 triplets per second since the repetition rate is equal to 10 Hz. We interpreted these results in the framework of a model we developed on the basis of the nonlinear momentum operator in the Heisenberg representation under the undepleted pump and stimulation approximation.
This article is devoted to the generation and the quantum correlations of triple photons, which correspond to the creation of three highly correlated photons from the splitting of a single photon by a phase-matched third-order parametric nonlinear process. These triples constitute a Greenberger–Horne–Zeilinger state of light and are interesting from a fundamental point of view but also for new schemes of quantum cryptography. We give here the classical and quantum descriptions of triple photon generation, we report on the first experimental demonstration of such a generation, and we calculate the Wigner function of three-photon quantum states of light.
Demonstrating quantum properties of triple photons generated by χ3\chi ^3χ3 processes
Abstract Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states. Graphic abstract
We report implementation and modelling of an efficient photon-triplets generation experiment based on a difference-frequency-mixing of two picosecond beams at 532 nm and 1491 nm in a type II phase-matched KTP crystal. The photon-triplets flux was measured as a function of the energy of the two incident beams using a coincidence protocol. A maximal flux of 11.6 photon-triplets per second was achieved. These experimental data were satisfactorily described by a semiclassical model based on the quantum fluctuations of vacuum and the classical equations of nonlinear optics.