Quantum steering is a kind of quantum correlations stronger than entanglement but weaker than Bell nonlocality. In an optomechanical system pumped by squeezed light and driven in the red sideband, we study—under thermal effects—stationary Gaussian steering and its asymmetry of two mechanical modes. In the resolved sideband regime using experimentally feasible parameters, we show that Gaussian steering can be created by quantum fluctuations transfer from the squeezed light to the two mechanical modes. Moreover, one-way steering can be observed by controlling the squeezing degree or the environmental temperature. A comparative study between Gaussian steering and Gaussian Rényi-2 entanglement of the two considered modes shows on one hand that both steering and entanglement suffer from a sudden death-like phenomenon with early vanishing of steering in various circumstances. On the other hand, steering is found stronger than entanglement, however, remains constantly upper bounded by Gaussian Rényi-2 entanglement, and decays rapidly to zero under thermal noise.

Einstein-Podolski-Rosen steering is a form of quantum correlation exhibiting an intrinsic asymmetry between two entangled systems. In this paper, we propose a scheme for examining dynamical Gaussian quantum steering of two mixed mechanical modes. For this, we use two spatially separated optomechanical cavities fed by squeezed light. We work in the resolved sideband regime. Limiting to the adiabatic regime, we show that it is possible to generate dynamical Gaussian steering via a quantum fluctuations transfer from squeezed light to the mechanical modes. By an appropriate choice of the environmental parameters, one-way steering can be observed in different scenarios. Finally, comparing with entanglement – quantified by the Gaussian Rényi-2 entropy, we show that Gaussian steering is strongly sensitive to the thermal effects and always upper bounded by entanglement degree.

Using the Gaussian Rényi-2 entropy, we analyse the behaviour of two different aspects of quantum correlations (entanglement and quantum discord) in two optomechanical subsystems (optical and mechanical). We work in the resolved sideband and weak coupling regimes. In experimentally accessible parameters, we show that it is possible to create entanglement and quantum discord in the considered subsystems by quantum fluctuations transfer from either light to light or light to matter. We find that both mechanical and optical entanglement are strongly sensitive to thermal noises. In particular, we find that the mechanical one is more affected by thermal effects than that optical. Finally, we reveal that under thermal noises, the discord associated with the entangled state decays aggressively, whereas the discord of the separable state (quantumness of correlations) exhibits a freezing behaviour, seeming to be captured over a wide range of temperature.

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 (2001 J. Phys. A: Math. Gen. 34 6899) 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.