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Quantum behavior of the Duffing oscillator at the dissipative phase transition

Author

Listed:
  • Qi-Ming Chen

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Michael Fischer

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Yuki Nojiri

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Michael Renger

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Edwar Xie

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Matti Partanen

    (Bayerische Akademie der Wissenschaften
    IQM)

  • Stefan Pogorzalek

    (Bayerische Akademie der Wissenschaften
    Technische Universität München
    IQM)

  • Kirill G. Fedorov

    (Bayerische Akademie der Wissenschaften
    Technische Universität München)

  • Achim Marx

    (Bayerische Akademie der Wissenschaften)

  • Frank Deppe

    (Bayerische Akademie der Wissenschaften
    Technische Universität München
    Munich Center for Quantum Science and Technology (MCQST)
    IQM)

  • Rudolf Gross

    (Bayerische Akademie der Wissenschaften
    Technische Universität München
    Munich Center for Quantum Science and Technology (MCQST))

Abstract

The non-deterministic behavior of the Duffing oscillator is classically attributed to the coexistence of two steady states in a double-well potential. However, this interpretation fails in the quantum-mechanical perspective which predicts a single unique steady state. Here, we measure the non-equilibrium dynamics of a superconducting Duffing oscillator and experimentally reconcile the classical and quantum descriptions as indicated by the Liouvillian spectral theory. We demonstrate that the two classically regarded steady states are in fact quantum metastable states. They have a remarkably long lifetime but must eventually relax into the single unique steady state allowed by quantum mechanics. By engineering their lifetime, we observe a first-order dissipative phase transition and reveal the two distinct phases by quantum state tomography. Our results reveal a smooth quantum state evolution behind a sudden dissipative phase transition and form an essential step towards understanding the intriguing phenomena in driven-dissipative systems.

Suggested Citation

  • Qi-Ming Chen & Michael Fischer & Yuki Nojiri & Michael Renger & Edwar Xie & Matti Partanen & Stefan Pogorzalek & Kirill G. Fedorov & Achim Marx & Frank Deppe & Rudolf Gross, 2023. "Quantum behavior of the Duffing oscillator at the dissipative phase transition," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-38217-x
    DOI: 10.1038/s41467-023-38217-x
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    References listed on IDEAS

    as
    1. Ruichao Ma & Brendan Saxberg & Clai Owens & Nelson Leung & Yao Lu & Jonathan Simon & David I. Schuster, 2019. "Author Correction: A dissipatively stabilized Mott insulator of photons," Nature, Nature, vol. 570(7761), pages 52-52, June.
    2. Ruichao Ma & Brendan Saxberg & Clai Owens & Nelson Leung & Yao Lu & Jonathan Simon & David I. Schuster, 2019. "A dissipatively stabilized Mott insulator of photons," Nature, Nature, vol. 566(7742), pages 51-57, February.
    3. Z.R. Lin & K. Inomata & K. Koshino & W.D. Oliver & Y. Nakamura & J.S. Tsai & T. Yamamoto, 2014. "Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits," Nature Communications, Nature, vol. 5(1), pages 1-6, December.
    4. Dykman, M.I. & Krivoglaz, M.A., 1980. "Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 480-494.
    5. Brendan Saxberg & Andrei Vrajitoarea & Gabrielle Roberts & Margaret G. Panetta & Jonathan Simon & David I. Schuster, 2022. "Disorder-assisted assembly of strongly correlated fluids of light," Nature, Nature, vol. 612(7940), pages 435-441, December.
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    Cited by:

    1. Jiang, Y.D. & Zhang, W. & Zhang, Y.F. & Bi, Q.S., 2024. "Bursting oscillations in coupling Mathieu-van der Pol oscillator under parametric excitation," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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