Complex Edge-State Phase Transitions in 1D Topological Laser Arrays

Abstract: We report the first observation of lasing in topological edge states in a 1D Su-Schrieffer-Heeger active array of resonators. We show that in the presence of chiral-time ($\mathcal{CT}$) symmetry, this non-Hermitian topological structure can experience complex phase transitions that alter the emission spectra as well as the ensued mode competition between edge and bulk states. The onset of these phase transitions is found to occur at the boundaries associated with the complex geometric phase- a generalized version of the Berry phase in Hermitian settings. Our experiments and theoretical analysis demonstrate that the topology of the system plays a key role in determining its operation when it lases: topologically controlled lasing.