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Entanglement signatures for quantum synchronization with single-ion phonon laser.

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    Quantum synchronization in a single-ion phonon laser shows maximum entanglement near the synchronization boundary. This phenomenon, linked to frequency entrainment and Liouvillian exceptional points (LEPs), offers new avenues for quantum applications.

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    Area of Science:

    • Quantum physics
    • Quantum optics
    • Nonlinear dynamics

    Background:

    • Quantum synchronization is a phenomenon where quantum systems exhibit synchronized behavior.
    • Phonon lasers, utilizing collective vibrations (phonons), are promising for quantum technologies.
    • External driving can manipulate quantum states and induce synchronization.

    Purpose of the Study:

    • To investigate the entanglement properties of a single-ion phonon laser under external driving.
    • To identify the conditions leading to maximum entanglement in this quantum system.
    • To explore the connection between entanglement, frequency entrainment, and Liouvillian exceptional points (LEPs).

    Main Methods:

    • Theoretical study of a single-ion phonon laser model.
    • Analysis of entanglement dynamics using quantum state evolution.
    • Investigation of Liouvillian eigenspectra to identify exceptional points.

    Main Results:

    • Maximum steady-state entanglement observed near the synchronization-unsynchronization boundary.
    • Entanglement exhibits oscillatory behavior during time evolution.
    • Frequency entrainment is evidenced by the bending of observed frequency and emergence of LEPs.

    Conclusions:

    • The study reveals a strong correlation between quantum synchronization, entanglement, and Liouvillian exceptional points.
    • LEPs are identified as a key indicator of frequency entrainment in quantum synchronization.
    • The findings suggest potential applications of LEPs in quantum synchronization technologies.