Topological pumping of light governed by Fibonacci numbers

Ruihan Peng; Kai Yang; Qidong Fu; Yanli Chen; Peng Wang; Yaroslav V. Kartashov; Vladimir V. Konotop; Fangwei Ye

doi:10.1186/s43593-025-00095-9

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Topological pumping of light governed by Fibonacci numbers

eLight Vol. 5, (2025)

Research Article | Updated：2025-12-17

- Topological pumping of light governed by Fibonacci numbers
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- DOI：10.1186/s43593-025-00095-9
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- Received：06 February 2025，
  
  Revised：2025-06-02，
  
  Accepted：14 June 2025，
  
  Published Online：05 August 2025，
  
  Published：2025-12
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Ruihan Peng, Kai Yang, Qidong Fu, et al. Topological pumping of light governed by Fibonacci numbers[J]. eLight, 2025, 5.
DOI：

Ruihan Peng, Kai Yang, Qidong Fu, et al. Topological pumping of light governed by Fibonacci numbers[J]. eLight, 2025, 5. DOI： 10.1186/s43593-025-00095-9.

摘要

Abstract

Topological pumping refers to transfer of a physical quantity governed by the system topology

resulting in quantized amounts of the transferred quantities. It is a ubiquitous wave phenomenon typically considered subject to exactly periodic adiabatic variation of the system parameters. Recently

proposals for generalizing quasi-periodic topological pumping and identifying possible physical settings for its implementation have emerged. In a strict sense

pumping with incommensurate frequencies can only manifest over infinite evolution distances

raising a fundamental question about its observability in real-world finite-dimensional systems. Here we demonstrate that bi-chromatic topological pumping with two frequencies

whose ratio is an irrational number

can be viewed as the convergence limit of pumping with two commensurate frequencies representing the best rational approximations of that irrational number. In our experiment

this phenomenon is observed as the displacement of a light beam center in photorefractive crystals induced by two optical lattices. The longitudinal periods of the lattices

that in the paraxial approximation emulate two pumping frequencies

are related as Fibonacci numbers

successively approaching the golden ratio. We observed that a one-cycle displacement of the beam center at each successive approximation is determined by the relation between successive Fibonacci numbers

while the average direction of propagation (emulating average pumping velocity) of the beam is determined by the golden ratio.

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references

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