• Photonics Research
  • Vol. 7, Issue 11, 1240 (2019)
Q. Zhong1、2, S. Nelson1、2, M. Khajavikhan3, D. N. Christodoulides3, and R. El-Ganainy1、2、*
Author Affiliations
  • 1Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
  • 2Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, Michigan 49931, USA
  • 3College of Optics & Photonics-CREOL, University of Central Florida, Orlando, Florida 32816, USA
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    DOI: 10.1364/PRJ.7.001240 Cite this Article Set citation alerts
    Q. Zhong, S. Nelson, M. Khajavikhan, D. N. Christodoulides, R. El-Ganainy. Bosonic discrete supersymmetry for quasi-two-dimensional optical arrays[J]. Photonics Research, 2019, 7(11): 1240 Copy Citation Text show less

    Abstract

    We apply the notion of discrete supersymmetry based on matrix factorization to quantum systems consisting of coupled bosonic oscillators to construct isospectral bosonic quantum networks. By using the algebra that arises due to the indistinguishability of bosonic particles, we write down the Schr dinger equations for these oscillators in the different boson-number sectors. By doing so, we obtain, for every partner quantum network, a system of coupled differential equations that can be emulated by classical light propagation in optical waveguide arrays. This mathematical scheme allows us to build quasi-two-dimensional optical arrays that are either isospectral or share only a subset of their spectrum after deliberately omitting some chosen eigenstates from the spectrum. As an example, we use this technique (which we call bosonic discrete supersymmetry or BD-SUSY) to design two optical, silica-based waveguide arrays consisting of six and three elements, respectively, with overlapping eigenspectrum.
    H^=βon=13a^na^n+κn=12a^na^n+1+H.c.,(1)

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    ida^dz=Ha^,H=[βoκ0κβoκ0κβo],(2)

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    QR=HβSI,HS=RQ+βSI,(3)

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    H^S=n=13Hn,nSa^na^n+n=12Hn,n+1Sa^na^n+1+H.c.(4)

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    H^=n=13λnA^nA^n,H^S=n=13λnB^nB^n,(5)

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    HS=[βo2κ02κβo000βo].(6)

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    H^RS=βo(a^1a^1+a^2a^2)+2κa^1a^2+H.c.(7)

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    H^RS=n=12μnB^nB^n,(8)

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    Q. Zhong, S. Nelson, M. Khajavikhan, D. N. Christodoulides, R. El-Ganainy. Bosonic discrete supersymmetry for quasi-two-dimensional optical arrays[J]. Photonics Research, 2019, 7(11): 1240
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