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 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 bandgap, topological transition, midgap topological edge and interface states in finite systems can all be achieved by controlled pumping. We also clarify non-Hermitian topological numbers and edge states in gapless conditions.