Topologically Tunable Polaritons Based on a Two-Dimensional Crystal in a Photonic Lattice

Structured optical cavities have advanced as a powerful test bed to study lattice Hamiltonians in general, and topological phenomena in particular. The in situ tuning of topological modes, enabled via substantial modifications of emulated lattice potentials, has remained out of experimental reach due to the commonly utilized monolithic cavity samples. Here, we study the Su-Schrieffer-Heeger (SSH) lattice Hamiltonian, which we emulate in a widely tunable open optical cavity strongly coupled to excitons in an integrated WS_{2} monolayer. The potential landscape comprises a topological domain boundary hosting a topological, exponentially localized mode at the interface between two lattices characterized by different Zak phases. The mode is spectrally tunable over 80 meV. Moreover, we use the unique tilt tunability of our implementation to transform the SSH lattice into a Stark ladder. This transformation couples the topologically protected defect mode to propagating lattice modes and effectively changes the symmetry of the system. Furthermore, it allows us to directly quantify the Zak-phase difference Δ_{Zak}=(1.07±0.11)π between the two topological phases. Our Letter constitutes an important step toward in situ tuning topological lattices to control and guide light on nonlinear chips.