We propose an effective approach for generating significant amount of entanglement and asymmetric steering between photon and phonon in a cavity magnomechanical system which consists of a microwave cavity and a yttrium iron garnet sphere. By driving the magnon mode of the yttrium iron garnet sphere with blue-detuned microwave field, the magnon mode can be acted as an engineered resevoir cools the Bogoliubov modes of microwave cavity mode and mechanical mode via beam-splitter-like interaction. In this way, the microwave cavity mode and mechanical mode are driven to two-mode squeezed states in the stationary limit. In particular, strong two-way and oneway asymmetric quantum steering between the photon and phonon modes can be obtained with even equal dissipation. It is very different from the conventional proposal of asymmetric quantum steering, where additional unbalanced losses or noises on the two subsystems has been imposed.Our finding may be significant to expand our understanding of the essential physics of asymmetric steering and extend the potential application of the cavity spintronics to device-independent quantum key distribution.

A theoretical scheme is proposed to generate significant amount of photon-phonon entanglement and asymmetric steering in a cavity magnomechanical system, which is constituted by trapping a yttrium iron garnet sphere in a microwave cavity. By applying a blue-detuned microwave driving field, we obtain an effective Hamiltonian where the magnon mode acting as an engineered resevoir cools the Bogoliubov modes of microwave cavity mode and mechanical mode via a beam-splitter-like interaction. By this means, the microwave cavity mode and mechanical mode can be driven to a two-mode squeezed state in the stationary limit. Particularly, strong two-way and one-way photon-phonon asymmetric quantum steering can be obtained with even equal dissipation. It is widely divergent with the conventional proposal, where additional unbalanced losses or noises should be imposed on the two subsystems. Our finding may be significant to expand our understanding of the essential physics of asymmetric steering and extend the potential application of the cavity spintronics to device-independent quantum key distribution.