Microscopic mechanism of level attraction

The emerging level attraction from dissipative light-matter coupling converges the typical Rabi-splitting feature from coherent coupling and exhibits potentials in topological information processing. However, the underlying microscopic quantum mechanism of dissipative coupling still remains unclear, which brings difficulties in quantifying and manipulating coherence-dissipation competition and thereby the flexible control of level attraction. Here, by coupling magnon to a cavity supporting both standing and travelling waves, we identify the travelling-wave state to be responsible for magnon-photon dissipative coupling. By characterizing radiative broadening of magnon linewidth, we quantify the coherent and dissipative coupling strengths and their competition. The effective magnon-photon coupling strength, as a net result of competition, is analytically presented in quantum theory to show good agreement with measurements. In this manner, we extend the control dimension of level attraction by tuning field torque on magnetization or global cavity geometry. Our finding opens new routines to engineer coupled harmonic oscillator system.