A finite SSH-chain has two topologically protected edge states for topologically non-trivial dimerization. By adiabatically changing the coupling strength and the on-site-potentials, these edge states can be transformed into each other (Thouless pump). In between each pump cycle the edge states become delocalized. At this point of the adiabatic transformation, small perturbations, e.g. a hole at one site, do not affect the edge-state exchange much.
We investigate how a commutation of neighboring sites will affect the state-exchange. Simulations and calculations show that only one of the edge states is affected by the perturbation. For an experiment it is necessary to be able to create a finite system where it is possible to act specifically on only a few sites to exchange their positions. We suggest using evanescently coupled waveguides. The light intensity along the propagation direction of these waveguides corresponds to the time evolution of a 2D quantum mechanical wave function.
To fabricate these waveguides we produce the inverse waveguide structure made of polymer by 3D-micro-printing (direct laser writing). After development we infiltrate the inverse structure with a material with higher refractive index . The on-site potential can be controlled via the radius of the waveguides and the coupling strength via the distance between them. The 3D-trajectories of the waveguides allow realizing a site-exchange by twisting a pair of strongly coupled waveguides around. Long propagation distance relative to the hopping distance is needed to ensure the transformation is adiabatic.
 Jörg, et al., New J. Phys. 19, 083003 (2017).
Julian Schulz, Christina Jörg, and Georg von Freymann, "Robustness of a Thouless pump in case of local site-exchange perturbations (Conference Presentation)," Proc. SPIE 10930, Advanced Fabrication Technologies for Micro/Nano Optics and Photonics XII, 109300P (Presented at SPIE OPTO: February 04, 2019; Published: 4 March 2019); https://doi.org/10.1117/12.2507833.6009872042001.
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