Experimental topological photonic superlattice

Topological phase, possessing inherent robustness against disorder, plays a central role in understanding matter, tailoring properties of artificial materials, and holding the promise of fault-tolerant quantum simulation and computing. Various topological phases and accessible controllability are being enthusiastically pursued in a wide spectrum ranging from condensed-matter to photonic systems. Recently, a topological photonic superlattice with arbitrary number of sites in each unit cell was proposed to provide richer topological properties. Here we successfully map such a multipartite structure into a photonic chip by using a femtosecond laser direct writing technique and demonstrate a direct observation of topological photonic superlattices in the quantum regime. Besides the tunable number of topologically protected edge states, we also observe stable interface states induced by the interference of topological linear modes, which exhibits Bloch-oscillation-like breathing dynamic behavior but free of nonlinearity.

Figure 1

Structure and spectrum of the superlattice. (a) The schematic of the superlattice. The superlattice with the nearest-neighbor coupling contains $M$ unit cells and $J$ sites in each cell. Therefore, there are $M\times J$ sites in the lattice. (b–e) The eigenspectra of superlattices which contain different site numbers $J=3$ and $J=4$. There are $J-1$ gaps in the band structure, and two edge sates in each gap for the topological nontrivial structure (c, e) but not for the trivial cases (b, d). (f) The spatial distributions of the bulk state and edge states of the superlattice with $J=3$. The photon is distributed in all the sites for the bulk state (i) but localized in the end of the lattice for the edge state (ii, iii). The parameters are picked as $\tau =0.7$ and $t=0.15$ in the calculation.

Figure 2

Experimental observation of edge states for superlattices. (a) The sketch of the experimental setup. Different superlattices are fabricated in the same photonic chip. Heralded single photons generated from the periodically poled potassium titanyl phosphate (PPKTP) crystal are injected into the lattices after being focused by a lens and collected at the output facet by an ICCD after being collimated. (b, c) The measured edge states of superlattices. Both the left (red) and right (blue) edge states of superlattices are observed for (b) $J=3$ and (c) $J=4$. The parameters picked in the experiment are the same as those in the simulation.

Figure 3

Topological interface states. The propagation-constant spectrum of superlattices (left) without and (right) with disorder with $J=4$ shows that there are three interface states in the gap. The band structure and the spatial distributions do not change much even after introducing the disorder. The parameters are picked as $\tau =0.7$, $t_1=t_3=0.2$, and $t_2=0.15$. The disorder is introduced by adding uniformly distributed random coupling strength varying from 0 to 0.1 for each coupling.

Figure 4

Direct observation of topological interface states. (a) The interface state forming a breathinglike oscillation owns the similar dynamic with Bloch oscillation. We observe a complete periodical dynamic in the experiment by measuring the output distribution under different evolution distance (1–6) varying from 20 to 45 mm with step size of 5 mm. (b) The stability of interface-state propagation against disorder is well experimentally demonstrated (i–vi). The parameters picked in the experiment are the same as those in the simulation.