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Journal of Physics B Atomic Molecular and Optical Physics

Quantum versus classical correlations in a double cavity optomechanical system

Abderrahim Lakhfif, Abdelkader Hidki, Jamal El Qars, Mostafa Nassik

Published Apr 24, 2022• 11 citations
Publisher

Abstract

Abstract 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.

DOI
10.1088/1361-6455/ac69bf

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Abstract 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.
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.
The aim of this paper is to quantify the quantum correlations between mechanical and optical modes in an optomechanical system with two spatially separated Fabry–Pérot cavities. We use logarithmic negativity [Formula: see text] and entanglement of formation (EoF), respectively, to quantify entanglement between optical and mechanical modes, while Gaussian geometric discord (GGD) is used to capture all nonclassical correlations, including entanglement. These quantifiers are evaluated as functions of the physical parameters characterizing the environment and the system (the thermal bath temperature [Formula: see text], the photons number [Formula: see text], the optomechanical cooperativity [Formula: see text], the squeeze parameter [Formula: see text] and the drive pump power [Formula: see text]). By considering recent experimental parameters, we show that GGD is more robust than entanglement for high thermal bath temperature and low optomechanical cooperativity. We also find that these quantifiers improve with increasing optomechanical cooperativity. The effects of the other parameters are also discussed in detail.
In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.
We study the dynamics of classical-quantum correlations in the nonadiabatic regime, using the rotating wave approximation (RWA), between two movable mirrors of two spatially separated Fabry–Pérot cavities, each of the two cavities having a movable end-mirror and coupled to a two-mode squeezed light from spontaneous parametric down-conversion. This work completes our previous work [M. Amazioug, M. Nassik and N. Habiballah, Eur. Phys. J. D 72, 171 (2018)] where we have studied the transfer of quantum correlations in steady state. The Bures distance is used to quantify the amount of entanglement of the symmetrical squeezed thermal state, and the Gaussian quantum discord is considered to quantify the quantumness of the quantum correlations even though the two movable mirrors are separable. Furthermore, total correlations are quantified using quantum mutual information. Indeed, these three indicators depend mainly on the temperature of the movable mirror and the squeezing parameter in strong coupling regime.
Abstract 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).
The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach three simultaneous bipartite entanglements via the quantum correlations transfer from the squeezed light to the system. While, even without squeezed light, the quantumness of correlations can be captured simultaneously between the three modes for a very wide range of parameters. Specifically, we find that the two optical modes exhibit more quantum correlations in comparison with the entangled mechanical–optical modes. Finally, unlike the two hybrid subsystems, the purely optical one seems more resilient against the environmental destructive effects.