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Laser Physics

Classical and quantum aspects of multimode parametric interactions

Alessia Allevi, Maria Bondani, Alessandro Ferraro, Matteo G. A. Paris

Published Sep 28, 2006• 27 citations
Publisher

Abstract

Parametric interactions in nonlinear crystals represent a powerful tool in the optical manipulation of information, both in the classical and the quantum regime. Here, we analyze in detail classical and quantum aspects of three-and five-mode parametric interactions in x (2) nonlinear crystals. The equations of motion are explicitly derived and then solved within the parametric approximation. We describe several applications, including holography, all-optical gates, generation of entanglement, and telecloning. Experimental results on the photon distributions and correlations of the generated beams are also reported and discussed.

DOI
10.1134/s1054660x06100082

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Parametric interactions in nonlinear crystals represent a powerful tool in the optical manipulation of information, both in the classical and the quantum regime. Here, we analyze in detail classical and quantum aspects of three-and five-mode parametric interactions in x (2) nonlinear crystals. The equations of motion are explicitly derived and then solved within the parametric approximation. We describe several applications, including holography, all-optical gates, generation of entanglement, and telecloning. Experimental results on the photon distributions and correlations of the generated beams are also reported and discussed.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.
Optics is arguably the most important branch of physics that has ever been studied. It is not only an essential ingredient of many other branches of physics that we study, it governs how we see, how we measure, and how we communicate in the modern world. And as the world continues to change, so do our tools and resources. In a relatively short amount of time, we have progressed from rudimentary tools that shape the world around us, to tools that harness the fundamental laws of nature. Unsurprisingly, the laws of nature governing optics remain paramount. This is because many of today's most advanced technologies rely on the classical and quantum properties of specially prepared beams of light. For example, there are quantum computing, quantum information, the quantum internet, quantum-enhanced metrology and quantum-enhanced imaging, to name a few. It is time to go a layer deeper in our understanding of these beams of light, particularly ones generated in nonlinear-optical interactions, since these are commonly the source of beams with quantum properties. The critical observation is that in each spatial mode (or spectral mode) of light exiting a nonlinear interaction, there are actually many transverse-spatial modes that have not been fully investigated. We use a Born-like approximation and a Green's function method to predict the classical mode structure of beams created during nonlinear interactions. Then, we extend the single-mode quantum theory by developing a second-quantization procedure of the classical modes. We derive an amplitude matrix, which governs the interaction between the modes and we calculate the evolution of the system. We show that our classical theory agrees nicely with experimental results, better than previous theories. Furthermore, we present simulations that predict ways to tailor the mode structure while adding, subtracting, and canceling orbital angular momentum transfer in nonlinear interactions. We use our quantum theory to predict the variance, covariance, the coupling of the modes, and how the noise suppression is distributed among the modes. In each case, we focus on exposing the underlying transverse spatial mode structure and suggest ways to tailor it depending on the intended use of the quantum resources. The simulations herein illustrate the utility of our theory, which is a convenient and powerful optimization tool. It can be used to show how the interplay of experimental beam parameters can influence the quantum properties of the beam(s) generated during the interaction. For example, the mode structure of the
The teleportation of entangled optical images is for the first time considered. The scheme offered is based on process of four-partite state generation in coupled parametric interactions realizing in an aperiodic nonlinear photonic crystal. The coupled nonlinear optical process consists of one parametric down-conversion process which is followed by two up-conversion ones. We study nonclassical properties of the generated fields by analyzing the EPR correlations for different pairs of modes and carry out the comparison of the EPR correlations of the input and images output images and also calculate fidelity of the teleportation exploiting the covariance matrices of the images. We take into account the difference of spatial frequency bandwidths of the entangled images and fields generated in the coupled process. It has been established that under certain parameters of the scheme one can be obtain rather high fidelity of the teleportation and good preservation of the quantum correlations of the input images for all details of the images.
We address the generation of fully inseparable three-mode entangled states of radiation by interlinked nonlinear interactions in χ(2) media. We show how three-mode entanglement can be used to realize symmetric and asymmetric telecloning machines, which achieve optimal fidelity for coherent states. An experimental implementation involving a single nonlinear crystal in which the two interactions take place simultaneously is suggested. Preliminary experimental results showing the feasibility and the effectiveness of the interaction scheme with a seeded crystal are also presented.
Type-II parametric down conversion in nonlinear optical crystals has turned out to be one of the most powerful methods to generate entangled photon pairs, and even allowed a large set of experiments on foundations of quantum mechanics and recent applications in quantum communication. In this paper, we present an experimental investigation of the emission characteristics for down-converted photons in order to investigate the possibility of high brightness sources for correlated photon pairs. Furthermore, we discuss possible ways to increase the collection efficiency for polarization entangled photon pairs.