Magneton bistability in quantum dot-double cavity optomechanical coupling system

Magnons, as quasiparticles arising from spin wave excitations in magnetic materials, have demonstrated significant application potential in quantum information technology, spintronics, and microwave engineering in recent years. The cavity magnon optomechanical system, serving as a key platform for investigating magneto-optical interactions, has advanced the exploration of nonlinear dynamical behaviors and the innovative design of quantum devices through strong coupling between magnons, photons, and phonons. However, traditional single-cavity systems face limitations in terms of tunability, long-range interactions, and nonlinear enhancement, making them insufficient for complex quantum control requirements. In recent years, dual-cavity systems have become a research hotspot due to their multidimensional control capabilities achieved through inter-cavity coupling, such as photon mode splitting and enhanced nonlinear Kerr effects. Meanwhile, semiconductor quantum dots, provide a novel pathway for regulating magnon dynamics due to their tunable nonlinear response characteristics. In this work, we construct a novel coupled quantum system by integrating quantum dots and a dual-cavity architecture, and investigate the bistable phenomena under both forward and backward driving field inputs. By comparing the third-order nonlinear equations governing magnon populations in the two scenarios, we derive the impedance matching condition. When this condition is satisfied, the magnon responses induced by forward driving field and backward driving field are identical. Conversely, under impedance mismatch, the magnon responses exhibit different behaviors. Specifically, when the impedance matching condition is violated, the dual-cavity magnon optomechanical system incorporating three-level quantum dot molecules exhibits a lower bistability threshold than its counterpart without quantum dots. This allows for a transition from low steady state to high steady state while reducing the driving field strength, thereby achieving switching functionality at lower input power. Furthermore, we establish a multiparameter cooperative control model, revealing a three-dimensional parameter space formed by tunneling coupling, cavity-quantum dot coupling, and inter-cavity coupling. By adjusting these coupling strengths, the bistability threshold and hysteresis loop width can be effectively controlled, thereby modulating the driving field intensity required for bistability. This system is expected to experimentally observe the magnonic bistability through the vector network analyzer-based detection of abrupt changes in transmission or absorption windows in reflection spectra. Such capabilities can advance data signal transmission, switching devices, and memory technologies, and has the potential to serve as components of large-scale quantum information processing units. Additionally, this research may find important applications in the field of magnetic spintronics.