$\mathcal{PT}$ Symmetric Non-Hermitian Cavity Magnomechanics

Abstract: We design and explore PT-symmetric behavior of a hybrid non-Hermitian cavity magnomechanics consisting of a ferromagnetic YIG sphere driven by external magnetic field. Non-Hermicity is engineered by using a traveling field directly interacting with YIG. The external magnetic field excites collective mechanical modes of magnons, which later excites cavity mode leading to a coupling between cavity magnons and photons. The magnomechanical interaction of the system also excites phonon and couple them to the system. By computing eigenvalue spectrum, we demonstrate the occurrence of three-order exceptional point emerge with the increase of magnon-photon coupling at a specific incidence angle of traveling field. We illustrate the unique bi-broken and uni-protected PT-symmetry regions in eigenvalue spectrum unlike previously investigated non-Hermitian system, which can be tuned with gain and loss configuration by manipulating ratio between traveling field strength and magnon-photon coupling. Interestingly, protected PT-symmetry only exists on the axis of exceptional point. We further show that the PT-symmetry can only be govern at two angle of incident of traveling field. However, later, by performing stability analysis, we illustrate that the system is only stable at $\pi/2$ and, on all other angles, either the system is non-PT-symmetric or it is unstable. Furthermore, we govern the parametric stability conditions for the system and, by defining stablity parameter, illustrate the stable and unstable parametric regimes. Our finding not only discusses a new type of PT-symmetric system, but also could act as foundation to bring cavity magnomechanics to the subject of quantum information and process.