Pulsed entanglement and quantum steering in a three-mode electro-optomechanical system
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Pulsed entanglement and quantum steering in a three-mode electro-optomechanical system M Mazaheri1
· S Jamasb2
Received: 16 May 2019 / Accepted: 8 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We investigate bipartite entanglement and quantum steering in a three-mode, hybrid electro-optomechanical system consisting of a Fabry–Perot optical cavity, a nanomechanical oscillator and a lumped-element microwave cavity. The nanomechanical resonator is directly coupled to the optical cavity on the one side via the moving mirror of the Fabry–Perot cavity, and on the other side, it is capacitively coupled to the microwave cavity. There is no direct coupling between the cavity modes. The optical cavity is blue-detuned through excitation by a laser source emitting short pulses, while the microwave cavity is red-detuned through excitation by a voltage pulse generator. The presence of bipartite entanglement between different modes is verified based on the asymmetric entanglement criteria. Specifically, the system is shown to behave effectively as a two-mode system in which a perfect bipartite EPR state can be formed by the optical cavity and the mirror. The possibility of generating genuine tripartite entanglement is also investigated by examining the necessary conditions for multiparty multimode entanglement. Simultaneous coupling of the three modes is shown to be possible in accordance with the genuine tripartite entanglement criteria. Furthermore, we establish the existence of quantum steering between the modes using the steering parameter formality and examine the monogamy relations to quantify the amount of bipartite steering shared between different modes. Notably, steering is found to be present only between the mechanical and the optical cavity modes. Keywords Cavity optomechanics · Entanglement · Quantum steering · Decoherence
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M Mazaheri [email protected]
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Department of Basic Science, Hamedan University of Technology, Hamedan 65169-1-3733, Iran
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Department of Biomedical Engineering, Hamedan University of Technology, Hamedan 65169-1-3733, Iran 0123456789().: V,-vol
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M. Mazaheri, S. Jamasb
1 Introduction In an electro-optomechanical system, optical and microwave cavity modes can be entangled by means of a macroscopic mechanical oscillator [1–4]. In these systems the radiation pressure of the cavity field can influence the motion of macroscopic objects such as a movable mirror or a drum-head capacitor plate such that parametric coupling between the cavity modes and the mechanical mode may result. Entanglement and squeezing represent the non-classical effects produced by such parametric coupling [4,5]. While a number of investigations have been undertaken to study entanglement in two-mode optomechanical systems [6–11], generation of entangled states in threemode systems has been less frequently investigated [12–15]. In systems consisting of more than two modes, complex correlations leading to multimode entanglement may result [4]. Thre
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