Synthesizing multi-dimensional excitation dynamics and localization transition in one-dimensional lattices

Abstract

The excitation dynamics in complex networks1 can describe the fundamental aspects of transport and localization across multiple fields of science, ranging from solid-state physics and photonics to biological signalling pathways and neuromorphic circuits2,3,4,5. Although the effects of increasing network dimensionality are highly non-trivial, their implementation likewise becomes ever more challenging due to the exponentially growing numbers of sites and connections6,7,8. To address these challenges, we formulate a universal approach for mapping arbitrary networks to synthesized one-dimensional lattices with strictly local inhomogeneous couplings, where the dynamics at the excited site is exactly replicated. We present direct experimental observations in judiciously designed planar photonic structures, showcasing non-monotonic excitation decays associated with up to seven-dimensional hypercubic lattices, and demonstrate a novel sharp localization transition specific to four and higher dimensions. The unprecedented capability of experimentally exploring multi-dimensional dynamics and harnessing their unique features in one-dimensional lattices can find multiple applications in diverse physical systems, including photonic integrated circuits.

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Fig. 1: Mapping multi-dimensional networks to 1D lattices.
Fig. 2: Experimental verification of synthesizing the excitation dynamics of a 2D structure in a 1D lattice.
Fig. 3: Experimental observation of excitation dynamics mapped from 1D, 3D and 7D hypercubic lattices.
Fig. 4: Sharp transition of defect localization in 4D and higher-dimensional hypercubic lattices and direct experimental evidence.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

This work was supported by the Australian Research Council (DP160100619, DP170103778 and DP190100277), the Australia–Germany Joint Research Cooperation Scheme, Erasmus Mundus (NANOPHI 2013 5659/002-001), the Alexander von Humboldt-Stiftung and the German Research Foundation (BL 574/13-1, SZ 276/15-1). A.S. acknowledges financial support from the Alfried Krupp von Bohlen und Halbach Foundation. K.W. acknowledges discussions with S. Fan and financial support from the Robert and Helen Crompton Award and SPIE Optics and Photonics Education Scholarship. The work of D.N.C. was partially supported by ARO (grant no. W911NF-17-1-0481), ONR (grant no. N00014-18-1-2347), the Qatar Foundation (NPRP9-020-1-006) and by US–Israel BSF (2016381). The work of A.E.M. was supported by the UNSW Scientia Fellowship. The authors also thank C. Otto for preparing the high-quality fused-silica samples used in all experiments presented here.

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The theory was developed by K.W., A.A.D., A.E.M., A.M., D.N.C. and A.A.S. The design, implementation and characterization of the lattice structure were carried out by L.J.M., M.E., M.H. and A.S. The project was supervised by A.S. and A.A.S. All authors discussed the results and co-wrote the paper.

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Correspondence to Alexander Szameit or Andrey A. Sukhorukov.

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Maczewsky, L.J., Wang, K., Dovgiy, A.A. et al. Synthesizing multi-dimensional excitation dynamics and localization transition in one-dimensional lattices. Nat. Photonics 14, 76–81 (2020). https://doi.org/10.1038/s41566-019-0562-8

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