Mode competition of a phonon laser induced by ultrastrong cavity-magnon coupling

In cavity magnomechanics, we find that the unique ultrastrong magnon-microwave photon interaction can induce mode competition in multimode phonon lasers, even though each mechanical mode is coupled to its respective driven magnon mode, which plays the similar role of the gain medium in the optical laser. Such a separate model corresponds to a richer phase diagram compared to that in which all modes are immersed in a common gain medium, in particular containing a second-order phase transition: the excited oscillator changes its behavior from suppression to absorption of the other oscillator's energy, leading to an obvious cooling by heating phenomenon. The mode competition phase transition also has a good correspondence with the synchronization phenomenon between the self-sustaining dynamics of the phonon modes. Finally, we discuss that the mode competition will be weakened as more modes are present in the system. Our work provides a foundation for related studies such as the self-sustaining dynamics of multibodies with complex structures.