  A primary motivation for studying topological matter regards the protection
of topological order from its environment. In this work, we study a topological
emitter array coupled to an electromagnetic environment. The photon-emitter
coupling produces nonlocal interactions between emitters. Using periodic
boundary conditions for all ranges of environment-induced interactions, the
chiral symmetry inherent to the emitter array is preserved. This chiral
symmetry protects the Hamiltonian, and induces parity in the Lindblad operator.
A topological phase transition occurs at a critical photon-emitter coupling
related to the energy spectrum width of the emitter array. Interestingly, the
critical point nontrivially changes the dissipation rates of edge states,
yielding a dissipative topological phase transition. In the protected
topological phase, edge states suffer from environment-induced dissipation for
weak photon-emitter coupling. However, strong coupling leads to robust
dissipationless edge states with a window at the emitter spacing. Our work
shows the potential to manipulate topological quantum matter with
electromagnetic environments.
