Free-Space Entangled Quantum Carpets

Abstract

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.

10 pages, 8 figures

References in corpus (5)

• Imaging high-dimensional spatial entanglement with a camera
• Introduction to the Transverse Spatial Correlations in Spontaneous Parametric Down-Conversion through the Biphoton Birth Zone
• Einstein-Podolsky-Rosen correlations from colliding Bose-Einstein condensates
• Quantum Information Processing by Weaving Quantum Talbot Carpets
• Fourier processing of quantum light

Cited by in corpus (8)

• Parameter estimation of time and frequency shifts with generalized HOM interferometry
• Testing for entanglement with periodic coarse-graining
• Practical computational advantage from the quantum switch on a generalized family of promise problems
• The Hong-Ou-Mandel experiment: from photon indistinguishability to continuous variables quantum computing
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Theory of Quantum Path Computing with Fourier Optics and Future Applications for Quantum Supremacy, Neural Networks and Nonlinear Schrödinger Equations
• Tomographic entanglement indicators in frequency combs and Talbot carpets
• Quantum carpets from Gaussian sum theory