Realization of Attractive Level Crossing via a Dissipative Mode

The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In strong interaction regime, such interaction usually gives rise to the level anti-crossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and is explained by a non-Hermitian model Hamiltonian. However, the mechanism of the such attractive coupling is still unclear. Here we reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third-party as the invisible cavity mode with large leakage in the cavity-magnon experiments. This understanding enables designing dissipative coupling in all sorts of coupled systems.