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

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. In order to accomplish this we engineered a fishnet metamaterial to have a negative refractive index at 780 nm. Here, 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.
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  1. Univ. of Vienna (Austria). Vienna Center for Quantum Science and Technoloy
  2. Univ. of California, Berkeley, CA (United States). Nanoscale Science and Engineering Center; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Univ. of Vienna (Austria). Vienna Center for Quantum Science and Technoloy; Univ. of Moncton, NB (Canada). Dept. of Physics and Astronomy
  4. Univ. of Vienna (Austria). Vienna Center for Quantum Science and Technoloy; Austrian Academy of Sciences, Vienna (Austria). Inst. for Quantum Optics and Quantum Information
Publication Date:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 8; Journal ID: ISSN 2041-1723
Nature Publishing Group
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
36 MATERIALS SCIENCE; metamaterials; quantum mechanics; quantum optics; single photons and quantum effects
OSTI Identifier: