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arXiv:1809.01176 · Journal of Physics B Atomic Molecular and Optical Physics

Creation of bipartite steering correlations by a fast damped auxiliary mode

Lihui Sun, Kaikai Zhang, Feng Xia, Bin Hu, Fang Chen, Chunchao Yu

Published Aug 10, 2018• 1 citation
arXivHTMLPDF

Abstract

Abstract We consider a three-mode system and show how steering correlations can be created between two modes of the system using the fast dissipation of the third mode. These correlations result in a directional form of entanglement, called quantum or Einstein–Podolsky–Rosen steering. We illustrate this on examples of the interactions among damped radiation modes in an optomechanical three-mode system. By assuming that one of the modes undergoes fast dissipation, we show that the coupling of that mode to one or two other modes of the system may result in one- or two-way quantum steering. Explicit analytical results are given for the steering parameters. We find that two modes coupled by the parametric-type interaction and damped with the same rates can be entangled but cannot exhibit quantum steering. When, in addition, one of the modes is coupled to a fast damped mode, steering correlations are created and the modes then exhibit one-way steering. The creation of the steering correlations is interpreted in the context of the variances of the quadrature components of the modes that the steering correlations result from an asymmetry in the variances of the quadrature components of the modes induced by the auxiliary mode. It is found that the fluctuations act directionally that quantum steering may occur only when the variance of the steering mode is larger that the variance of the steered mode. The scheme is shown to be quite robust against the thermal excitation of the modes if the fluctuations of the steering mode are larger than the fluctuations of the steered mode.

DOI
10.1088/1361-6455/aad987

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Abstract We consider a three-mode system and show how steering correlations can be created between two modes of the system using the fast dissipation of the third mode. These correlations result in a directional form of entanglement, called quantum or Einstein–Podolsky–Rosen steering. We illustrate this on examples of the interactions among damped radiation modes in an optomechanical three-mode system. By assuming that one of the modes undergoes fast dissipation, we show that the coupling of that mode to one or two other modes of the system may result in one- or two-way quantum steering. Explicit analytical results are given for the steering parameters. We find that two modes coupled by the parametric-type interaction and damped with the same rates can be entangled but cannot exhibit quantum steering. When, in addition, one of the modes is coupled to a fast damped mode, steering correlations are created and the modes then exhibit one-way steering. The creation of the steering correlations is interpreted in the context of the variances of the quadrature components of the modes that the steering correlations result from an asymmetry in the variances of the quadrature components of the modes induced by the auxiliary mode. It is found that the fluctuations act directionally that quantum steering may occur only when the variance of the steering mode is larger that the variance of the steered mode. The scheme is shown to be quite robust against the thermal excitation of the modes if the fluctuations of the steering mode are larger than the fluctuations of the steered mode.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation and its intrinsic asymmetry makes it distinct from entanglement and Bell nonlocality. We propose here a scheme for realizing one-way Gaussian steering of two electromagnetic fields mediated by a mechanical oscillator. We reveal that the steady-state one-way steering of the intracavity and output fields is obtainable with different cavity losses or strong mechanical damping. The conditions for achieving this asymmetric steering are found, and it shows that the steering is robust against thermal mechanical fluctuations. The present scheme can realize hybrid microwave-optical asymmetric steering by optoelectromechanics. In addition, our results are generic and can also be applied to other three-mode parametrically coupled bosonic systems.
Conditions for experimental detection of asymmetric one-way quantum steering in a three-mode optomechanical system are examined. We consider cases of collective steering in which two modes collectively interact with the third mode, and the case of separate modes steering in which two mutually independent modes interact with the third mode. We find that the occurrence of both collective and separate modes quantum steering results not from an asymmetry between thermal noise of the modes, as it has been realized in linear optics systems, but from an asymmetry between the damping rates of the modes. We show the requirement that the modes are damped with different rates to be the necessary and sufficient condition for collective steering. In the case of separate modes, we find that apart from unequal damping rates, an additional condition is required that the modes are coupled to the third mode with unequal strengths. Thus, the generation of quantum steering between separate modes is more restrictive to the parameters than the collective steering. Determination of conditions for experimental detection of one-way steering in multi-mode system could give a new stimulus to develop secure directional communication networks.
We consider a three-mode optomechanical system in which two mechanical oscillators are independently coupled to a cavity mode driven by two controllable lasers. By controlling the two-tone driving, one can prepare the entanglement and Einstein-Podolsky-Rosen (EPR) steering of two mechanical modes, in which the cavity mode acts as a single reservoir to cool two Bogoliubov modes. We find that the direction of EPR steering can be manipulated effectively by adjusting the damping rates and the thermal noises of two mechanical modes. In addition, we show that the entanglement and EPR steering between two mechanical modes can be enhanced by adding a parametric amplifier (PA) into the cavity. The effects of the strength and phase of the PA on the mechanical entanglement and EPR steering are analyzed and discussed in detail. Meanwhile, the additional PA can also expand the region of the one-way steering and strengthen the robustness of the entanglement and EPR steering against the thermal noise. The present scheme may provide effective resources for quantum information processing.
Einstein-Podolsky-Rosen steering manifests a type of quantum correlations intermediate between entanglement and Bell nonlocality. In this paper we propose a scheme for realizing hybrid atom-mechanical quantum steering in the steady-state regime. In our scheme, an optomechanical two-mode cavity is coupled to a distant ensemble of double-$\ensuremath{\lambda}$ atoms in a cascade way, which induces the dissipative interaction between the mechanics and the internal atomic states. We show that strong cavity dissipation can lead to two-way atom-mechanical steering and the optimal steering exhibited in an approximate two-mode squeezed-vacuum atom-mechanical state. Moreover, we find that for the present cascade coupling scheme, the one-way steering from the mechanical oscillator to the atoms is achievable under certain conditions, while the reverse one-way steering is impossible to obtain. The reason for achieving the asymmetric steering is analyzed and the effect of mechanical thermal noise on the steering is also studied.
Abstract Einstein–Podolsky–Rosen (EPR) steering as a form of quantum correlation lies between entanglement and Bell nonlocality and exhibits an inherent asymmetry between two observers. We study EPR steering of two fields, which are generated via four-wave mixing processes and are entangled with each other due to the dissipation of the atomic reservoir. It is shown that the one-way steering happens from one mode to the other for different cavity decay rates and not too small cooperation parameters. Depending on the adiabatic and nonadiabatic conditions, the one-way steering occurs in a different detuning region when the cooperation parameters are relatively small. An increase in the cooperation parameters leads to an increase both in the parameter region and in the degree for the one-way steering. Finally we generalize the present scheme to the cases of the bright and/or collective fields.
We study multipartite entanglement, the generation of Einstein-Podolsky-Rosen (EPR) states, and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beam-splitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold, the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two-way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.