Fig. 1. Band structure of the Su–Schrieffer–Heeger model. (A) The SSH model describes a one-dimensional lattice with alternating nearest-neighbor couplings. For d=0, the chain becomes homogenous. (B) Band structure of an infinite SSH chain. Any nonzero dimerization opens up a band gap. (C) Energy eigenvalues for a finite SSH chain terminated at a weak bond. A topological edge state of zero energy (marked light pink) resides in the band gap.

Fig. 2. Experimental setup. (A) Direct laser writing technique: femtosecond-laser pulses are focused into a moving glass sample, forming a waveguide trajectory. (B) Waveguide structure, consisting of an incoupling fanning, the actual SSH waveguide lattice with alternating couplings, and a fan-out. The lattice can be excited in the bulk, at the trivial and topological edge. (C) The full experimental setup consists of a spontaneous parametric down conversion (SPDC) photon pair source, fiber arrays that couple the photons into and out of the functional structure on the chip, and avalanche photodetectors.

Fig. 3. Intensity propagation at the lattice edges. The figures on the left show the simulated intensity evolution along the z axis when the edge is excited, and on the right the measured output intensities at the end of the lattice are depicted. (A) At the topological edge, light propagates from the edge into the bulk, in contrast to (B) the trivial edge, where part of the edge state is excited and intensity remains in the edge waveguide. (C) In the homogenous array, there is no edge state and the intensity is transported into the bulk ballistically.

Fig. 4. Correlations in the SSH lattice. Two indistinguishable photons are launched into neighboring sites of a lattice at the topological edge, trivial edge, and bulk. The coincidence counts after the quantum walk are shown in the upper row, and the corresponding theory is depicted below. For comparison, a homogenous lattice is investigated on the right. On the topological edge, the photons tend to remain in the edge state, which clearly shows in the measurement. The diagonal elements of the correlation matrices are not accessible without photon number resolution and are therefore masked gray in the simulations.

Fig. 5. Inter-particle distance. Histogram for the distance between the photon pairs detected in the quantum walk (see Fig. 4). At the topological edge, one of the photons tends to remain in the edge state, leading to a higher inter-particle distance than at the trivial edge, where the photons tend to remain in close proximity. Note that due to the use of avalanche photodiodes as detectors, the cases in which both photons arrive in the same channel are systematically inaccessible in the experiments, preventing a normalization of the inter-particle distance distributions. Further deviations can be attributed to imperfections of the synthesized input state due to the limited accuracy of the polarization alignment between the two injection fibers.

Fig. 6. Hong–Ou–Mandel dip of the photon pair source. The retrieved coincidence counts (pink) were fitted with a Gaussian function (black), characterizing the visibility at 94%±2%.

Fig. 7. Additional simulations of intensity propagation for classical light launched into the edge neighboring waveguides.