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

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.