Magnomechanical phonon laser beyond the steady state

Phonon lasers, the mechanical analogs of optical lasers, have long been a subject of interest as they provide coherent sound waves. We numerically study a magnomechanical phonon laser that operates under a general continuous-wave pump. This system consists of a microwave cavity, a sphere of magnetic material (yttrium iron garnet), a microwave drive pump, and a uniform external bias magnetic field. A population inversion between the supermodes of the system leads to phonon laser action. We study the population inversion and the stimulated emission of phonons under various conditions, such as different drive pump powers and detunings. Unlike previous studies, our results show that the population inversion between the supermodes oscillates with time. Despite the oscillations of the population inversion, one can achieve relatively large stimulated phonon emission if the power of the drive pump is beyond a threshold. Moreover, the optimum operation occurs if the frequency of the drive field matches the frequencies of the cavity photons and magnons. Since it is highly tunable with low loss and has an extra degree of freedom provided by the constant magnetic field, it is possible to develop the system into an alternative to the optomechanical phonon lasers.