Free-Space Entangled Quantum Carpets

• Published in: arXiv.org
• Main Authors: Barros, Mariana R, Ketterer, Andreas, Osvaldo Jiménez Farías, Walborn, Stephen P
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 23.02.2017
• Subjects: Bell's inequality; Carpets; Computer simulation; Matter waves; Photons; Physics - Quantum Physics; Quantum phenomena; Quantum theory; Superposition (mathematics); Talbot effect
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1702.07391

The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as "quantum carpets", corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a \(D\)-level qudit, in such a way that the Talbot effect can be used to process the \(D\)-dimensional quantum information [Far\'ıas et al, PRA (2015)]. Here we introduce a scheme to produce free-propagating "entangled quantum carpets" with pairs of photons produced by spontaneous parametric down-conversion. First we introduce an optical device that can be used to synthesize arbitrary superposition states of Talbot qudits. Sending spatially entangled photon pairs through a pair of these devices produces an entangled pair of qudits. As an application, we show how the Talbot effect can be used to test a \(D\)-dimensional Bell inequality. Numerical simulations show that violation of the Bell inequality depends strongly on the amount of spatial correlation in the initial two-photon state. We briefly discuss how our optical scheme might be adapted to matter wave experiments.