Fast mode competition of multi-mode phonon lasers enhanced by optical gain in an active MIM system

Multi-mode phonon lasers have emerged as a pivotal research direction and have achieved remarkable progress in recent years. However, multi-mode phonon lasers exhibit slower mode competition during the startup process relative to optical lasers, which hinders their extensive application. To solve this conundrum, we explore such mode competition in an MIM system with optical gain, i.e., an active MIM system. A dissipative coupling model for this active membrane in the middle (MIM) system is established. As a result, we achieve fast mode competition with the relaxation time decreased by approximately 100 times compared to the existing system [ Phys. Rev. Lett. 113 , 030802 ( 2014 ) 10.1103/PhysRevLett.113.030802 ]. In addition, the coherence of phonons during the mode competition process is observed for the first time to the best of our knowledge. Our work will benefit from the rapid stabilization of single-mode phonon lasers, thereby facilitating the research and practical applications, such as high-stability phonon lasers, multi-mode phonon lasers, and phonon laser frequency combs.