Fig. 3

Observation of the exceptional point in cavity magnon–polaritons. a Measured total output spectrum vs. the displacement of the YIG sphere in the cavity. b Calculated total output spectrum corresponding to the measured results in a. Corresponding coupling strength is indicated according to the relation g _m/2π = 1.3\(\left| x \right|\). In a, b, the open-circle curves are the eigenfrequencies calculated using Eq. (3). c Dependance of the total output spectrum on Δϕ. d Dependance of the total output spectrum on the power ratio. For the three curves (I, II, and III) in c, d, the corresponding locations in a are marked with crosses (red, green, and navy). e Phase transition between the magnetically induced transparency (MIT) regime and the weak-coupling regime. The black open-circle curve corresponds to the minima of the total output transmission vs. the displacement of the YIG sphere, where each value in the MIT and strong-coupling regions is the average value of the two minima of the two CPA branches at a given displacement