  We experimentally examine the topological nature of a strongly coupled
spin-photon system induced by damping. The presence of both spin and photonic
losses results in a non-Hermitian system with a variety of exotic phenomena
dictated by the topological structure of the eigenvalue spectra and the
presence of an exceptional point (EP), where the coupled spin-photon
eigenvectors coalesce. By controlling both the spin resonance frequency and the
spin-photon coupling strength we observe a resonance crossing for
cooperativities above one, suggesting that the boundary between weak and strong
coupling should be based on the EP location rather than the cooperativity.
Furthermore we observe dynamic mode switching when encircling the EP and
identify the potential to engineer the topological structure of coupled
spin-photon systems with additional modes. Our work therefore further
highlights the role of damping within the strong coupling regime, and
demonstrates the potential and great flexibility of spin-photon systems for
studies of non-Hermitian physics.
