$\mathcal{PT}$ 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 $π/2$ 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.

Figures (4)

• Figure 1: Schematic diagram of the non-hermitian cavity magnomechanical system. A YIG sphere is placed inside a microwave cavity driven by a strong magnetic field $\eta$ exciting magnons $\hat{m}$, which coupling with the cavity photons $\hat{a}$ (having frequency $\omega_a$) oscillating at $\omega_m$. Magnomechanical interactions also excite phonon $\hat{b}$ from YIG with frequency $\omega_b$. To make system non-Hermitain, a traveling field interacts with YIG at angle $\theta$ and strength $\Gamma$.
• Figure 2: Eigenvalue spectrum as a function of normalized magnon-photon coupling $G_{ma}/\Delta_a$, the blue solid line is the real part $Re[\lambda]$ while the red dashed line is for the imaginary part $Im[\lambda]$ of the eigenvalue. Here $G_{ma}/\Delta_a=1$ and $\Gamma/\omega_b=1$. (a) and (b) are for the incidence angles of $\theta=pi/2$ and $\theta=\pi$ if traveling field, respectively. The other parameters that we choose are $\kappa_a/\Delta_a=0.08,\kappa_m/\Delta_m=0.08, G_{mb}/\Delta_a=0.09, \gamma_b/\Delta_a=1/1000.$
• Figure 3: (a), (b), (c) and (d) are eigenvalue spectrum as a function of normalized $G_{ma}/\Delta_a$. The incident angle $\theta=pi/2$ for (a) and (b), while $\theta=\pi$ for (c) and (d), respectively. The solid line is $\Gamma/\omega_b=1$, the dashed line is $\Gamma/\omega_b=2$. (e) and (f) are 3D plot of the eigenvalue with respect to non-hermitian strength $\Gamma/\omega_b$ and magnon-photon coupling $G_{ma}/\Delta_a$, at angle $\theta=pi/2$ and $\theta=\pi$, respectively. The other parameters are the same as in Fig.\ref{['fig2']}.
• Figure 4: Stability parameter $\mathcal{S}$ as the function of magnon-photon coupling $G_{ma}$ and effective magnon-phonon coupling $G_{mb}$. (a) and (b) are for non-hermitian strength $\Gamma/\omega_b=1.0$, while (c) and (d) are for $\Gamma/\omega_b=2.0$, respectively. (e) and (f) illustrates $\mathcal{S}$ versus $\kappa_a/\Delta_a$ and $\kappa_m/\Delta_m$ at fixed $G_{ma}/\Delta_a=\Gamma/\omega_b=1$. The incident angle considered in plots is $\theta=pi/2$. The numerical parameters are as in Fig.\ref{['fig2']}