Observation of Floquet solitons in a topological bandgap

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Science  22 May 2020:
Vol. 368, Issue 6493, pp. 856-859
DOI: 10.1126/science.aba8725

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Topological insulators go nonlinear

Whereas solid-state insulators tend to be fixed by material properties, photonic topological insulators can be designed at will to mimic a variety of scenarios and complex interactions. Mukherjee and Rechtsman go beyond the linear optical regime that has been studied to date and show that photonic topological insulators can also exhibit nonlinear optical features (see the Perspective by Ablowitz and Cole). Their array of laser-written waveguides can support solitons, which are also found to exhibit topological features, performing cyclotron-like orbits associated with the topology of the lattice. The nonlinear properties provide a rich playground for further exploration, with the possibility of mimicking other interacting bosonic systems.

Science, this issue p. 856; see also p. 821


Topological protection is a universal phenomenon that applies to electronic, photonic, ultracold atomic, mechanical, and other systems. The vast majority of research in these systems has explored the linear domain, where interparticle interactions are negligible. We experimentally observed solitons—waves that propagate without changing shape as a result of nonlinearity—in a photonic Floquet topological insulator. These solitons exhibited distinct behavior in that they executed cyclotron-like orbits associated with the underlying topology. Specifically, we used a waveguide array with periodic variations along the waveguide axis, giving rise to nonzero winding number, and the nonlinearity arose from the optical Kerr effect. This result applies to a range of bosonic systems because it is described by the focusing nonlinear Schrödinger equation (equivalently, the attractive Gross-Pitaevskii equation).

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