Evolution of Renyi-2 quantum correlations in a double cavity-magnon system

This work reports on the stationary evolution of three different kinds of quantum correlations between two distant magnon modes. The system at hand consists of two spatially separated cavities, where each cavity has a microwave (MW) cavity and a magnon mode. The two cavities are coupled to each other via the photon-tunneling process, and both are exposed to the output field of a squeezed vacuum MW fields source. By calculating the covariance matrix fully describing the state of the two magnon modes, we give the explicit expressions of the measures of correlations defined via the Renyi-2 entropy, i.e. the Gaussian quantum steering G, Gaussian Renyi-2 entanglement E-R and Gaussian Renyi-2 mutual information I-R. We find that, the quantum steering is always upper bounded by the entanglement, which is in turn always upper bounded by half of the total correlations. The obtained results are consistent with the hierarchical Renyi-2 quantum correlations established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117, 220502 (2016)], i.e. they fulfill the hierarchical inequality (1/2)I-R & GE; E-R & GE;G. The influences of the squeezing parameter, the environmental temperature, the cavity-magnon coupling and the cavity-cavity coupling on the correlations are studied in detail.