Polarization-dependent topology in quantum emitter chains

The role of polarization in the topology of quantum emitter chains is investigated theoretically, whereby "polarization" refers to the transition dipole moments of the emitters. We show that, if the chain is zigzag-shaped, different topological phases can be realized by adjusting the polarization direction. It turns out that long-range dipole-dipole couplings weaken the bulk-boundary correspondence, but on the other hand give rise to higher-order topological phases with four observable edge modes. We also demonstrate how the polarization orientation can be used to define an additional dimension and simulate a synthetic Chern insulator. Our findings open up a way to actively switch between various topological phases within a single arrangement of quantum emitters.