We report on temporal evolution of three different kinds of correlations present between two mechanical resonators of two distant Fabry-Pérot cavities. The two cavities are jointly fed by a two-mode squeezed light and driven by two independent coherent lasers. We consider the initial state of the two mechanical modes as a two-mode uncorrelated thermal state. After evaluating the dynamical covariance matrix elements, we give explicit expressions of the measures of correlations defined via the Rényi-2 entropy, namely, the Rényi-2 quantum mutual information, the Gaussian Rényi-2 entanglement and the Gaussian quantum steering. We find that by an appropriate choice of the system parameters, it is possible to generate entanglement and steering via a quantum correlations transfer from squeezed light to the mechanical bi-mode state. The influence of the squeezing parameter, the optomechanical cooperativity and the environmental thermal noise on the correlations are studied thoroughly. Additionally, we show in various circumstances that the considered temporal correlations respect the hierarchical relation established in L Lami, C Hirche, G Adesso, and A Winter, (2016 Phys. Rev. Lett.
117, 220 502).
In a bipartite quantum state, where the total correlations can be divided into classical and quantum parts, Henderson and Vedral [J. Phys. A: Math. Gen. 34, 6899 (2001)] have conjectured that classical correlations should not be less than quantum ones. Here, we consider two symmetrical states of two driven optomechanical cavities coupled to a squeezed photon source and exposed to Markovian noise and damping. The total and quantum correlations are systematically quantified by quantum mutual information and quantum discord respectively. Interestingly, we analytically demonstrate that classical correlations in the considered two-mode Gaussian states are always superior to quantum ones, whatever the physical and environmental parameters are. Moreover, using experimentally accessible parameters, we show numerically the existence of a domination of classical correlations over quantum ones under various circumstances. Finally, we found that quantum, as well as classical correlations, have similar behaviors under the effect of thermal decoherence, squeezing and optomechanical coupling. Yet, classical correlations are more strong and robust.
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