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The European Physical Journal D

Entanglement, EPR steering and Gaussian geometric discord in a double cavity optomechanical systems

Mohamed Amazioug, Mostafa Nassik, Nabil Habiballah

Published Oct 1, 2018• 34 citations
Publisher
DOI
10.1140/epjd/e2018-90151-6

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We investigate the generation of quantum correlations between mechanical modes and optical modes in an optomechanical system, using the rotating wave approximation. The system is composed of two Fabry–Pérot cavities separated in space; each of the two cavities has a movable end-mirror. Our aim is the evaluation of entanglement between mechanical modes and optical modes, generated by correlations transfer from the squeezed light to the system, using Gaussian intrinsic entanglement as a witness of entanglement in continuous variables Gaussian states, and the quantification of the degree of mixedness of the Gaussian states using the purity. Then, we quantify nonclassical correlations between mechanical modes and optical modes even beyond entanglement by considering Gaussian geometric discord via the Hellinger distance. Indeed, entanglement, mixdness, and quantum discord are analyzed as a function of the parameters characterizing the system (thermal bath temperature, squeezing parameter, and optomechanical cooperativity). We find that, under thermal effect, when entanglement vanishes, purity and quantum discord remain nonzero. Remarkably, the Gaussian Hellinger discord is more robust than entanglement. The effects of the other parameters are discussed in detail.
We study the dissipative dynamics and the formation of entangled states in a driven cascaded quantum network, where a cascaded double-cavity optomechanical system is coupled to a common unidirectional optical fiber. In terms of two coherent laser fields simultaneously driving the chiral coupling system, the entanglement can be effectively transferred from the light to two nanomechanical resonators (NMRs) through cavity modes based on the completely destructive interference of quantum noise. By adjusting the relative strength ratio of red- and blue-detuned pump lasers, it is found that the two NMRs can be driven into a mixed two-mode Gaussian entangled mechanical state rather than a non-Gaussian entangled dark state or a pure entangled dark state. If the frequency of the NMR is tuned to be much larger than the chiral coupled-cavity-chain damping rate, it is demonstrated that the chiral dissipative cascaded system can always realize one-way Einstein-Podolsky-Rosen (EPR) steering from one mechanical oscillator to the other, while the reverse one-way EPR steering is impossible to obtain, and the reason for achieving asymmetric Gaussian steering is analyzed. Furthermore, a simple one-way EPR steering criterion based on two-photon correlation can be achieved for an arbitrary bipartite Gaussian state under the standard form of EPR steering, and the effect of mechanical thermal noise on the steering is also discussed. Moreover, the present chiral system can be realized with currently available experimental technology; therefore, we hope that it can be very helpful for potential applications in quantum computation and quantum communication.