Photonic Topological Insulating Phase Induced Solely by Gain and Loss

We reveal a one-dimensional topological insulating phase induced solely by gain and loss control in non-Hermitian optical lattices. The system comprises units of four uniformly coupled cavities, where the successive two have loss; the others experience gain, and they are balanced under two magnitudes. The gain and loss parts are effectively dimerized, and a bulk band gap, topological transition, midgap topological edge, and interface states in finite systems can all be achieved by controlled pumping. We also clarify non-Hermitian topological invariants and edge states in gapless conditions.