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Comptes Rendus Physique

Triple photons: a challenge in nonlinear and quantum optics

Kamel Bencheikh, Fabien Gravier, Julien Douady, Juan Ariel Levenson, Benoı̂t Boulanger

Published Sep 15, 2006• 59 citations
Publisher

Abstract

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.

DOI
10.1016/j.crhy.2006.07.014

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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 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.
We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second-order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show, for example, the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show robust, seeding-dependent, genuine triple-photon entanglement in the fully seeded case.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.
We will present our recent results in the generation of triple photons as well as triple slits, both providing interesting perspectives on the foundations of quantum mechanics and quantum optics. The creation of correlated triple photons [1] is a highly desirable process for research on quantum optics, novel states of three-photon entanglement, and applications in quantum information processing. It was proposed over 20 years ago, but considered impossible to perform given the low conversion efficiencies in non-linear optics. We recently managed to solve the technical challenges, and demonstrate a source for correlated photon triplets. Strikingly, the interferences of single photons passing through a triple slit can be useful for experimental verification of Born’s rule, which is at the heart of the formalism of quantum mechanics. We will illustrate the background of the argumentation, and show the elegant experimental setup, which allows this direct test of Born’s rule [2].