Nonreciprocal transparency windows, Fano resonance, and slow/fast light in a membrane-in-the-middle magnomechanical system induced by the Barnett effect

Abstract

Nonreciprocal phenomena are currently a major focus of research within the fields of classical and quantum technology. In this work, we theoretically investigate the interplay among multiple magnomechanically induced transparency (MMIT) windows, Fano resonances, slow/fast light, and nonreciprocal absorption and group delay in a hybrid cavity magnomechanical system. This system is composed of two yttrium iron garnet (YIG) spheres and a membrane positioned at the center of the cavity. By analyzing the absorption spectrum of a weak probe field in the presence of a strong control field, we demonstrate the emergence of five transparency windows resulting from combined photon-phonon, photon-magnon, and phonon-magnon interactions. The photon-phonon coupling associated with the membrane plays a crucial role in enhancing and tailoring these transparency features. We further examine the impact of the Barnett effect on the absorption and dispersion characteristics, showing that it enables the controllable manipulation of transparency windows and the generation of tunable Fano resonance profiles. The influence of cavity decay and magnon dissipation rates on the spectral response is also analyzed. In addition, we demonstrate that the group delay of the transmitted probe field can be effectively tuned via the photon-phonon coupling strength and the Barnett effect, allowing for a controllable transition between slow and fast light regimes. Finally, nonreciprocal absorption and group delay are achieved through appropriate adjustment of the coupling parameters. These findings highlight the potential of the proposed hybrid system for applications in optical signal processing and quantum information technologies.

Figures (9)

• Figure 1: (a) Schematic representation of a hybrid cavity magnomechanical platform. The system comprises two ferromagnetic yttrium iron garnet (YIG) spheres and a mechanical membrane placed inside a microwave cavity, which is driven by an external probe field at frequency $\omega_{p}$. A uniform magnetic field applied along the z-axis excites the collective spin-wave (magnon) modes in each YIG sphere, which are strongly coupled to the cavity electromagnetic field. Furthermore, the bias magnetic field activates the magnetostrictive effect, thereby inducing magnon-phonon coupling within both YIG spheres and enabling coherent interactions among the cavity, magnon, and mechanical modes. However, the sphere $m_1$ is directly driven by an external microwave field applied along the y-direction (control field). The rotation of the YIG sphere at an angular frequency $\omega_{B}$ generates an effective magnetic field $H_{B}$, which induces a frequency shift in magnon $m_1$. (b) Diagram showing the couplings among the various modes of our system. (c) The insets show the rotation directions of the YIG sphere, which induce angular frequency shifts of $\pm\Delta_{B}$ through the Barnett effect. (d) Variation of $H_B$ as a function of $|\Delta_B|/\omega_{b}$ for different magnon rotation directions about the z-axis.
• Figure 2: Real part of the output field $\epsilon_{\mathrm{R}}$ as a function of $\delta/\omega_{b}$. (a) $g_{1}=g_{2}=G_{1}=G_{2}=G_a=0$; (b) $g_{2}=G_{1}=G_{2}=G_a=0$ with $g_{1}/2\pi = 1.5$ MHz; (c) $g_{2}=G_{2}=G_a=0$ and $g_{1}/2\pi = G_{1}/2\pi = 1.5$ MHz; (d) $G_{2}=G_a=0$ with $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5$ MHz; (e) $G_a=0$ with $G_{2}/2\pi = 3.5$ MHz and $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5$ MHz; (f) $G_{a}/2\pi = 2.5$ MHz with $g_{1}/2\pi = g_{2}/2\pi = G_{2}/2\pi = 1.5$ MHz and $G_{2}/2\pi = 3.5$ MHz. All remaining parameters are given in the Table \ref{['Tab']}
• Figure 3: Imaginary part of the output field $\epsilon_{\mathrm{I}}$ as a function of $\delta/\omega_{b}$. (a) $g_{1}=g_{2}=G_{1}=G_{2}=G_a=0$; (b) $g_{2}=G_{1}=G_{2}=G_a=0$ with $g_{1}/2\pi = 1.5$ MHz; (c) $g_{2}=G_{2}=G_a=0$ and $g_{1}/2\pi = G_{1}/2\pi = 1.5$ MHz; (d) $G_{2}=G_a=0$ with $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5$ MHz; (e) $G_a=0$ with $G_{2}/2\pi = 3.5$ MHz and $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5$ MHz; (f) $G_{a}/2\pi = 2.5$ MHz with $g_{1}/2\pi = g_{2}/2\pi = G_{2}/2\pi = 1.5$ MHz and $G_{2}/2\pi = 3.5$ MHz. All remaining parameters are given in the Table \ref{['Tab']}.
• Figure 4: Real part of the output field $\epsilon_{\mathrm{R}}$ as a function of the normalized detuning $\delta/\omega_{b}$ for different coupling strengths: (a) varying $G_{1}$ with $g_{1}/2\pi = g_{2}/2\pi = 1.5~\text{MHz}$, $G_{2}/2\pi = 3.5~\text{MHz}$, $G_{a}/2\pi = 2.5~\text{MHz}$ and $\Delta_{B}=0$; (b) varying $G_{2}$ with $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5~\text{MHz}$, $G_{a}/2\pi = 3~\text{MHz}$ and $\Delta_{B}=0$; (c) varying $g_{1}$ with $G_{1}/2\pi = g_{2}/2\pi = 1.5~\text{MHz}$, $G_{2}/2\pi = 3.5~\text{MHz}$, $G_{a}/2\pi = 2.5~\text{MHz}$ and $\Delta_{B}=0$; (d) varying $g_{2}$ with $G_{1}/2\pi = g_{1}/2\pi = 1.5~\text{MHz}$, $G_{2}/2\pi = 3.5~\text{MHz}$, $G_{a}/2\pi = 2.5~\text{MHz}$ and $\Delta_{B}=0$; and (e) varying $G_{a}$ with $g_{1}/2\pi = g_{2}/2\pi = G_{1}/2\pi = 1.5~\text{MHz}$, $G_{2}/2\pi = 3.5~\text{MHz}$ and $\Delta_{B}=0$. All remaining parameters are provided in the Table \ref{['Tab']}.
• Figure 5: Real part of the output field $\epsilon_{\mathrm{R}}$ as a function of $\delta/\omega_{b}$ for different values of: (a) the cavity decay rate, (b) the dissipation rate of magnon $m_{1}$, and (c) the dissipation rate of magnon $m_{2}$, with $g_{1}/2\pi = g_{2}/2\pi=G_{1}/2\pi = 1.5~\text{MHz}$, $G_{2}/2\pi = 3.5~\text{MHz}$, and $G_{a}/2\pi = 3~\text{MHz}$. All remaining parameters are given in the Table \ref{['Tab']}.