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    Phase-selective tripartite entanglement and asymmetric Einstein-Podolsky-Rosen steering in squeezed optomechanics

    Ya-Feng Jiao1,2, Jie Wang3, Dong-Yang Wang4, Lei Tang5, Yan Wang1,2, Yun-Lan Zuo6, Wan-Su Bao7,*, Le-Man Kuang2,3,†, and Hui Jing2,3,‡

    • 1School of Electronics and Information, Zhengzhou University of Light Industry, Zhengzhou 450001, China
    • 2Academy for Quantum Science and Technology, Zhengzhou University of Light Industry, Zhengzhou 450001, China
    • 3Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
    • 4School of Physics, Zhengzhou University, Zhengzhou 450001, China
    • 5College of Physics and Electronic Engineering, Institute of Solid State Physics, Sichuan Normal University, Chengdu 610101, China
    • 6School of Physics and Chemistry, Hunan First Normal University, Changsha 410205, China
    • 7Henan Key Laboratory of Quantum Information and Cryptography, IEU, Zhengzhou 450001, China

    • *Contact author: bws@qiclab.cn
    • †Contact author: lmkuang@hunnu.edu.cn
    • ‡Contact author: jinghui73@gmail.com

    Phys. Rev. A 112, 012421 – Published 23 July, 2025

    DOI: https://doi.org/10.1103/m28c-8ggl

    Abstract

    The generation and manipulation of multipartite entanglement and Einstein-Podolsky-Rosen (EPR) steering in macroscopic systems not only play a fundamental role in exploring the nature of quantum mechanics, but are also at the core of current developments of various nascent quantum technologies. Here we report a theoretical method using squeezing-phase-controlled quantum noise flows to selectively generate and manipulate quantum entanglement and asymmetric EPR steering in a nonlinear χ(2) whispering-gallery-mode (WGM) optomechanical resonator. We show that by pumping the χ(2) nonlinear medium with two-photon optical fields and broadband squeezed lights, a pair of counterpropagating squeezed optical modes could be introduced to the WGM resonator, each coupled with an independent squeezed vacuum reservoir. This configuration could enable squeezing-phase-controlled light-reservoir interaction for each squeezed optical mode, providing a flexible tool for tailoring asymmetric optical noise flows in the counterpropagating modes. Based on this unique feature, it is found that with the injection of asymmetric noise flows, the generation of various types of bipartite and tripartite entanglement become phase-dependent, and thus they can be produced in an asymmetric way. More excitingly, it is also found that by further properly adjusting the squeezing parameters, the overall asymmetry of EPR steering can also be stepwise driven from a no-way regime, to a one-way regime, to a two-way regime. These findings, holding promise for preparing rich types of entangled quantum resources with asymmetric features, may have potential applications in the area of secure quantum information processing such as quantum secure direct communication and one-way quantum computing.

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