Single-photon test of hyper-complex quantum theories using a metamaterial

Lorenzo M. Procopio, Lee A. Rozema, Zi Jing Wong, Deny R. Hamel, Kevin O’Brien, Xiang Zhang (), Borivoje Dakić and Philip Walther ()
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Lorenzo M. Procopio: Vienna Center for Quantum Science and Technology, University of Vienna
Lee A. Rozema: Vienna Center for Quantum Science and Technology, University of Vienna
Zi Jing Wong: Nanoscale Science and Engineering Center, University of California
Deny R. Hamel: Vienna Center for Quantum Science and Technology, University of Vienna
Kevin O’Brien: Nanoscale Science and Engineering Center, University of California
Xiang Zhang: Nanoscale Science and Engineering Center, University of California
Borivoje Dakić: Vienna Center for Quantum Science and Technology, University of Vienna
Philip Walther: Vienna Center for Quantum Science and Technology, University of Vienna

Nature Communications, 2017, vol. 8, issue 1, 1-9

Abstract: Abstract In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to choose them over real numbers or generalizations of complex numbers, that is, hyper-complex numbers. Experiments performed to date have proven that real numbers are insufficient, but the need for hyper-complex numbers remains an open question. Here we experimentally probe hyper-complex quantum theories, studying one of their deviations from complex quantum theory: the non-commutativity of phases. We do so by passing single photons through a Sagnac interferometer containing both a metamaterial with a negative refractive index, and a positive phase shifter. To accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. We show that the metamaterial phase commutes with other phases with high precision, allowing us to place limits on a particular prediction of hyper-complex quantum theories.

Date: 2017
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DOI: 10.1038/ncomms15044

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