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Physical Review A

Steady-state light-mechanical quantum steerable correlations in cavity optomechanics

Huatang Tan, Wenwu Deng, Qing-Lin Wu, Gao‐xiang Li

Published May 16, 2017• 32 citations
Publisher

Abstract

Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect which is intrinsically distinct from Bell nonlocality and quantum entanglement. In this paper, we investigate in detail the properties of steady-state light-mechanical Gaussian steerable correlations in a generic cavity optomechanical system. When considering the steering between the intracavity field and the mechanical oscillator, we find that under blue-detuned driving, the steady-state steering via optomechanical parametric downconversion is present in only one direction and, moreover, the steering direction is determined merely by the relative dissipation strength of the cavity to the mechanics. Furthermore, when considering the steering between the cavity output field and the mechanical oscillator, we reveal that under red-detuned driving, strong steering can be achieved in the sideband-unresolved regime for a filtered output field with given central frequency and bandwidth. This steering with the output field can also be present in one way by adjusting the driving strength and exists up to the environment temperature $T\ensuremath{\approx}10$ K for the parameters close to those in the recent experiments. Finally, we show that the achieved strong light-mechanical correlations can be explored to realize macroscopic EPR steering of two distant optomechanical oscillators in the regime of unresolved sidebands via entanglement swapping.

DOI
10.1103/physreva.95.053842

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Modern Physics Letters A•Feb 9, 2024•1 citation
Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect which is intrinsically distinct from Bell nonlocality and quantum entanglement. In this paper, we investigate in detail the properties of steady-state light-mechanical Gaussian steerable correlations in a generic cavity optomechanical system. When considering the steering between the intracavity field and the mechanical oscillator, we find that under blue-detuned driving, the steady-state steering via optomechanical parametric downconversion is present in only one direction and, moreover, the steering direction is determined merely by the relative dissipation strength of the cavity to the mechanics. Furthermore, when considering the steering between the cavity output field and the mechanical oscillator, we reveal that under red-detuned driving, strong steering can be achieved in the sideband-unresolved regime for a filtered output field with given central frequency and bandwidth. This steering with the output field can also be present in one way by adjusting the driving strength and exists up to the environment temperature T\ensuremath≈10T\ensuremath{\approx}10T\ensuremath≈10 K for the parameters close to those in the recent experiments. Finally, we show that the achieved strong light-mechanical correlations can be explored to realize macroscopic EPR steering of two distant optomechanical oscillators in the regime of unresolved sidebands via entanglement swapping.
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.
Abstract In this paper, we propose a continuous measurement and feedback scheme to achieve strong Einstein–Podolsky–Rosen (EPR) steering and Bell nonlocality of two macroscopic mechanical oscillators in cavity optomechanics. Our system consists of two optomechanical cavities in which two cavity fields are coupled to each other via nondegenerate parametric downconversion. The two cavity output fields are subject to continuous Bell-like homodyne detection and the detection currents are fed back to drive the cavity fields. It is found that when the feedback is absent, the two mechanical oscillators can only be prepared in steady weakly entangled states which however do not display EPR steering and Bell nonlocality, due to the so-called 3 dB limit. But when the feedback is present, it is found that the mechanical entanglement is considerably enhanced such that strong mechanical steering and Bell nonlocality can be obtained in the steady-state regime. We analytically reveal that this is because the feedback drives the mechanical oscillators into a steady approximate two-mode squeezed vacuum state, with arbitrary squeezing in principle. It is shown that the feedback can also obviously improve the purity of the nonclassical mechanical states. The dependences of the mechanical quantum nonlocality on the feedback strength and thermal fluctuations are studied, and it is found that Bell nonlocality is much more vulnerable to thermal noise than EPR steerable nonlocality.
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.
We investigate under which conditions quantum nonlocal manifestations such as Einstein-Podolsky-Rosen steering or Bell nonlocality can manifest themselves even at the macroscopic level of two mechanical resonators in optomechanical systems. We adopt the powerful scheme of reservoir engineering, implemented by driving a cavity mode with a properly chosen two-tone field, to prepare two mechanical oscillators in an entangled state. We show that large and robust (both one-way and two-way) steering could be achieved in the steady state with realistic parameters. We analyze the mechanism of the asymmetric nature of steering in our system of a two-mode Gaussian state. However, unlike steering, a Bell nonlocality is present under much more stringent conditions. We consider two types of measurements, displaced parity and on-off detection, respectively. We show that for both the measurements the Bell violation requires very low environmental temperature. For the parity detection, a large Bell violation is observed only in the transient state when the mechanical modes decouple from the optical mode and with extremely small cavity losses and mechanical damping. However, for the on-off detection, a moderate Bell violation is found in the steady state and is robust against cavity losses and mechanical damping. Although a Bell violation with parity detection seems extremely challenging to demonstrate experimentally, the conditions required for violating Bell inequalities with the on-off detection are much less demanding.
Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocal effect that characterizes the ability to remotely control quantum states of one system via local measurements on another distant system entangled with the controlled one. Entanglement swapping is an effective way to realize distant entanglement, which is useful for building quantum networks. Previous studies show that the presence of entanglement of subsystems in mixed states is merely necessary for achieving entanglement swapping. In this paper, we find that for Gaussian entanglement swapping with two pairs of entangled modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}\phantom{\rule{4pt}{0ex}}(j=1,2)$, the existence of directional EPR steering from the modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}$ under homodyne detection to the other modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ is a sufficient and necessary condition for achieving swapped entanglement between modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}$, and moreover this achievement is independent of the reverse steering from modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{j}$ to ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}}_{j}$. We further reveal that this is because the steering in that direction enables the amplitude and phase squeezing of the two composite modes of modes ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{2}$ via homodyne detection, which is necessary and sufficient for swapped entanglement. As a concrete example, we next investigate light-mechanical steering in a dispersively or dissipatively coupled optomechanical system, and we consider the generation of entanglement between two distant optomechanical oscillators via entanglement swapping by utilizing steering. It is interesting to find that even without the constraint that the cavity linewidth should be smaller than the mechanical frequency, robust mechanical entanglement can be obtained in the steady-state regime.
Einstein–Podolsky–Rosen steering is a form of inseparable quantum correlations that exhibits an inherent asymmetric property, i.e. one-way steering. In this paper, we show that the radiation pressure effect can be profitably exploited to generate stationary Gaussian quantum steering between an optical cavity mode and a mechanical mode. The optical mode is driven by a blue-detuned laser within the unresolved sideband regime. Under realistic experimental conditions, we show that strong asymmetric steering can be generated between the two considered modes. Besides, we show that the direction of one-way steering can be controlled by varying the physical parameters of the system at hand (coupling, dissipation, and detuning). Also, we discuss how the generated steering can be estimated experimentally. The demonstrated optomechanical steering may have practical implications for asymmetric quantum information tasks, e.g. one-sided device-independent quantum key distribution and quantum teleportation.