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The possibility for detecting energy entanglement in normal metal -superconductor junctions is examined. For the first time we proved that twoelectrons in a NS structure originating from the same Cooper pair are entangledin the energy subspace. This work follows previous works where spinentanglement was studied in similar circuits. The device consists of asuperconducting beam splitter connected to two electronic Mach-Zehnderinterferometers. In each arms of the interferometers, energies are filteredwith coherent quantum dots. In contrast to previous studies of zero-frequencycross-correlations of electrical currents for this system, attention is drawnto finite-time measurements. This allows to observe two-particle interferencefor particles with different energies above and below Fermi level. Entanglementis first characterized via the concurrence for the two-particle spatial densitymatrix. Next, we formulate the Bell inequality, which is written in terms offinite-time noise correlators, and thereby we find a specific set of parametersfor which entanglement can be detected.Comment: 14 pages, 6 figure

Energy entanglement in normal metal–superconducting forks