Topological pumping over a photonic Fibonacci quasicrystal

Abstract

Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping-one of the hallmarks of topological states of matter-was recently realized for photons in a one-dimensional off-diagonal Harper model implemented in a photonic waveguide array. However, if the relationship between topological pumps and quasiperiodic systems is generic, one might wonder how to observe it in the canonical and most studied quasicrystalline system in one dimension-the Fibonacci chain. This chain is expected to facilitate a similar phenomenon, yet its discrete nature hinders the experimental study of such topological effects. Here, we overcome this obstacle by utilizing the topological equivalence of a family of quasiperiodic models which ranges from the Fibonacci chain to the Harper model. Implemented in photonic waveguide arrays, we observe the topological properties of this family, and perform a topological pumping of photons across a Fibonacci chain.

Measuring topological invariants from generalized edge states in polaritonic quasicrystals

“…From a general viewpoint, wave or quantum systems possessing a gapped energy spectrum, such as band insulators, superconductors, or 2D conductors in a magnetic field, can be assigned topological invariants generally called Chern numbers [3]. These numbers control a variety of physical phenomena: for instance in the integer quantum Hall effect, they determine the value of the Hall conductance as a function of magnetic field [4,5] [22,[28][29][30] and exploited to implement topological pumping, a key concept of topology [22]. A paradigmatic example of quasicrystal is given by the 1D Fibonacci chain.…”

“…In particular the topological edge states [25][26][27] of quasicrystals have been recently investigated in photonic systems [22,[28][29][30] and exploited to implement topological pumping, a key concept of topology [22]. A paradigmatic example of quasicrystal is given by the 1D Fibonacci chain.…”

“…These integers can take N distinct values, N being the number of letters in the chain [34]. Despite important advances on the topological properties of quasicrystals [19][20][21][22][23][24][28][29][30] the topological invariants have not yet been directly measured as winding numbers.…”

Experimental measurement of the Berry curvature from anomalous transport

“…In photonics, for example, topological edge states have been studied in a wide variety of (effectively) 1D set-ups, such as quantum walks 14 and pumping in optical quasicrystals 13,29,30 , as well as in 2D quantum Hall-like systems of photonic crystals 9-11 , propagating waveguides 12 and silicon ring resonators 15,16 . However, while the existence of such edge states is linked to the non-trivial global topological properties of bulk bands, a direct measurement of the Berry curvature itself has so far not been realized.…”

Robust unidirectional transport in a one-dimensional metacrystal with long-range hopping

“…In one-dimensional (1D) systems, the possibility of realizing robust one-way transport has received less attention so far, mainly because topological protection is generally unlikely in 1D. Proposals include 'Thouless pumping' in quasicrystals [25,26], Landau-Zener transport in binary lattices [27] ,the use of 'synthetic' dimensions in addition to the physical spatial dimension [28][29][30], and non-Hermitian transport [31]. In 1D lattices with short-range hopping, the action of synthetic gauge fields is generally trivial, as any loop encloses zero flux, and thus topological protection can arise from the adiabatic change of some parameter (Thouless pumping) or by adding a 'synthetic' dimension.…”