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Journal of Physics B Atomic Molecular and Optical Physics

Entanglement, uncertainty and dispersion: a simple experimental demonstration of non-classical correlations

Stefan Lerch, Thiago Guerreiro, Bruno Sanguinetti, Pavel Sekatski, Nicolas Gisin, André Stefanov

Published Jan 20, 2017• 6 citations
Publisher

Abstract

Abstract We perform an experiment to verify the presence of entanglement in photon pairs. By sending down-converted light through dispersive media with opposite group velocity dispersion coefficients, we overcome the minimum broadening of temporal correlation for classical light. Entanglement is proved via an inequality derived directly from Heisenberg’s uncertainty principle. We present a criterion to select a suitable down-conversion source. Moreover, we introduce a new method to analyze the temporal correlations between the entangled photons.

DOI
10.1088/1361-6455/aa5b19

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Abstract We perform an experiment to verify the presence of entanglement in photon pairs. By sending down-converted light through dispersive media with opposite group velocity dispersion coefficients, we overcome the minimum broadening of temporal correlation for classical light. Entanglement is proved via an inequality derived directly from Heisenberg’s uncertainty principle. We present a criterion to select a suitable down-conversion source. Moreover, we introduce a new method to analyze the temporal correlations between the entangled photons.
We derive an inequality bounding the strength of temporal correlations for a pair of light beams prepared in a separable state and propagating through dispersive media with opposite signs of group-velocity dispersion. The presented inequality can be violated by entangled states of light, such as photon pairs produced in spontaneous parametric down-conversion. Because the class of separable states covers the entire category of classical fields as a particular case, this result provides an unambiguously quantum feature of nonlocal dispersion cancellation that cannot be reproduced within the classical theory of electromagnetic radiation.
Following Einstein, Podolsky, and Rosen (EPR) original argument, we derive a pair of inequalities for the uncertainties in the sum of the momenta and in the difference of the positions of an entangled two-particle system. We prove that only entangled systems can satisfy both EPR-inequalities, in violation of the limits imposed by classical statistics. We propose an operational approach that allows applying the EPR inequalities to two-photon systems, as well. In particular, we demonstrate a scheme that allows implementing the EPR gedanken-experiment and verifying the EPR inequalities on systems of pairs of photons. We report the experimental results obtained in this kind of quantum interference and imaging experiment: SPDC two-photon system satisfies both EPR inequalities. The experimental verification of the EPR inequalities represents a practical way to experimentally distinguish entanglement from classical correlation in momentum and/or position variables for systems of two particles/photons. We emphasize the practical consequences of the EPR inequalities: only entanglement allows one to go beyond the limitations imposed by Heisenberg uncertainty on systems of classically correlated particles/photons. In this context we review a recent experiment of two-photon diffraction and quantum lithography.
This chapter describes three experiments to test and demonstrate the principles of quantum mechanics using correlated photons. These include the demonstration that the photon exists; production and measurement of entangled states of photons, including a measurement of a violation of a Bell inequality; and the interference of a single photon with itself and the quantum eraser. The experiments are presented in order of difficulty. In a birefringent medium, spontaneous parametric down-conversion occurs due to the interaction of the light and the medium. The analysis given can be generalized to show that the down-converted photons are created in planes other than the horizontal plane. All the down-converted photons of a given wavelength form a cone about the pump-beam axis, but photons in each pair follow, by conservation of momentum, correlated paths in the cone. The down-converted photons are created in a cone about the pump-beam direction. The experiment uses the horizontal slice of the down-conversion cone that contains the pump beam.
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations enable quantum technologies, including quantum computing or communication, while revealing the limits of our classical worldview by violating local realism. Given its importance in modern quantum science, we present this tutorial addressing the questions: What is entanglement, how does it differ from classical correlations, and how can it be experimentally verified? Using celebrated examples, such as Schrödinger's cat, we highlight the distinction between classical and quantum correlations and illustrate the definition of entangled and separable states. We review entanglement criteria by discussing Heisenberg-type uncertainty relations for continuous variables and the CHSH inequality for discrete systems. Focusing on concepts of quantum correlations and operational entanglement witnesses, we provide accessible tools and illustrative examples aimed at demystifying entanglement for a broad readership.