Enhancement of Steady Quantum Entanglement and Directional Controllability of Quantum Steering in Cavity Magnetic Hybrid Systems

Quantum entanglement (QE) and quantum steering (QS) are of importance for quantum information processing and computation. Though there are several schemes proposed for their realization, how to increase their degrees encounters a great challenge. In the present manuscript, it is proposed to enhance steady QE and control Gaussian QS for two magnons using a two-photon field acting on either magnon. The cavity-magnetic hybrid system consists of a microwave cavity in which two identical Yttrium-iron-garnet spheres are placed and the cavity is driven by a Josephson parametric amplifier (JPA) so as to generate steady QE and control Gaussian QS for the two Kittel modes. Besides, a two-photon driving field acting on either magnon in order to enhance the degree of QE and the ability of QS. The best condition to maximum entanglement and steering degrees for the two magnon modes at epsilon approximate to 0.8$\varepsilon \approx 0.8\nobreakspace $MHz and r approximate to 2$r \approx 2$ is found via the competitive relationship between the two-photon driving and JPA. Furthermore, it is revealed that steering direction for the two magnons can be controlled not only by the ratio between the two photon-magnon coupling parameters but also by the two-photon driving field, making controllable steering direction become easier.