  Bulk-edge correspondence, with quantized bulk topology leading to protected
edge states, is a hallmark of topological states of matter and has been
experimentally observed in electronic, atomic, photonic, and many other
systems. While bulk-edge correspondence has been extensively studied in
Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian
topological band theory due to the interplay between non-Hermiticity and
topology; and its effect on bulk-edge correspondence is still an ongoing
pursuit. Importantly, including non-Hermicity can significantly expand the
horizon of topological states of matter and lead to a plethora of unique
properties and device applications, an example of which is a topological laser.
However, the bulk topology, and thereby the bulk-edge correspondence, in
existing topological edge-mode lasers is not well defined. Here, we propose and
experimentally probe topological edge-mode lasing with a well-defined
non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring
resonators. By modeling the Hamiltonian with an additional degree of freedom
(referred to as synthetic dimension), our 1D structure is equivalent to a 2D
non-Hermitian Chern insulator with precise mapping. Our work may open a new
pathway for probing non-Hermitian topological effects and exploring
non-Hermitian topological device applications.
