Quantum transport in fractal networks

Xiao Yun Xu; Xiao Wei Wang; Dan Yang Chen; C. Morais Smith; Xian Min Jin

doi:10.1038/s41566-021-00845-4

Quantum transport in fractal networks

Xiao Yun Xu, Xiao Wei Wang, Dan Yang Chen, C. Morais Smith, Xian Min Jin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Fractals are fascinating, not only for their aesthetic appeal but also for allowing the investigation of physical properties in non-integer dimensions. In these unconventional systems, many intrinsic features might come into play, including the fractal dimension and the fractal geometry. Despite abundant theoretical studies, experiments in fractal networks remain elusive. Here we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices. We unveil the transport properties through the photon evolution patterns, the mean square displacement and the Pólya number. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. In addition, the critical point at which there is a transition from normal to anomalous transport depends on the fractal geometry. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics in great detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality.

Original language	English
Pages (from-to)	703-710
Number of pages	9
Journal	Nature Photonics
Volume	15
Issue number	9
DOIs	https://doi.org/10.1038/s41566-021-00845-4
Publication status	Published - Sept 2021

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s41566-021-00845-4Final published version, 2.35 MBLicence: Taverne

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title = "Quantum transport in fractal networks",

abstract = "Fractals are fascinating, not only for their aesthetic appeal but also for allowing the investigation of physical properties in non-integer dimensions. In these unconventional systems, many intrinsic features might come into play, including the fractal dimension and the fractal geometry. Despite abundant theoretical studies, experiments in fractal networks remain elusive. Here we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices. We unveil the transport properties through the photon evolution patterns, the mean square displacement and the P{\'o}lya number. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. In addition, the critical point at which there is a transition from normal to anomalous transport depends on the fractal geometry. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics in great detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality.",

author = "Xu, {Xiao Yun} and Wang, {Xiao Wei} and Chen, {Dan Yang} and Smith, {C. Morais} and Jin, {Xian Min}",

note = "Funding Information: We thank J.-W. Pan for helpful discussions, X.-L. Huang and Z.-M. Li for helping in the experiments, J. Gao, R.-J. Ren and S. Freeney for proof reading, and W.-H. Zhou for assistance in formatting the figures. This research is supported by the National Key R&D Program of China (2019YFA0308700, 2019YFA0706302 and 2017YFA0303700); National Natural Science Foundation of China (NSFC) (11904229, 61734005, 11761141014, 11690033); Science and Technology Commission of Shanghai Municipality (STCSM) (20JC1416300, 2019SHZDZX01); Shanghai Municipal Education Commission (SMEC) (2017-01-07-00-02-E00049); China Postdoctoral Science Foundation (2021M692094, 2020M671091). X.-M.J. acknowledges additional support from a Shanghai talent program and support from Zhiyuan Innovative Research Center of Shanghai Jiao Tong University. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Limited.",

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Quantum transport in fractal networks

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