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Quantum theory of Bloch oscillations in a resistively shunted transmon

Author

Listed:
  • Vladislav D. Kurilovich

    (Yale University
    Google Research)

  • Benjamin Remez

    (Yale University)

  • Leonid I. Glazman

    (Yale University)

Abstract

A transmon qubit embedded in a high-impedance environment acts in a way dual to a conventional Josephson junction. In analogy to the AC Josephson effect, biasing of the transmon by a direct current leads to the oscillations of voltage across it. These oscillations are known as the Bloch oscillations. We find the Bloch oscillations spectrum, and show that the zero-point fluctuations of charge make it broadband. Despite having a broad-band spectrum, Bloch oscillations can be brought in resonance with an external microwave radiation. The resonances lead to steps in the voltage-current relation, which are dual to the conventional Shapiro steps. We find how the shape of the steps depends on the environment impedance R, parameters of the transmon, and the microwave amplitude. The Bloch oscillations rely on the insulating state of the transmon which is realized at impedances exceeding the Schmid transition point, R > RQ = h/(2e)2.

Suggested Citation

  • Vladislav D. Kurilovich & Benjamin Remez & Leonid I. Glazman, 2025. "Quantum theory of Bloch oscillations in a resistively shunted transmon," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-56411-x
    DOI: 10.1038/s41467-025-56411-x
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    References listed on IDEAS

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    1. Fabian Kaap & Christoph Kissling & Victor Gaydamachenko & Lukas Grünhaupt & Sergey Lotkhov, 2024. "Demonstration of dual Shapiro steps in small Josephson junctions," Nature Communications, Nature, vol. 15(1), pages 1-6, December.
    2. Diego Subero & Olivier Maillet & Dmitry S. Golubev & George Thomas & Joonas T. Peltonen & Bayan Karimi & Marco Marín-Suárez & Alfredo Levy Yeyati & Rafael Sánchez & Sunghun Park & Jukka P. Pekola, 2023. "Bolometric detection of Josephson inductance in a highly resistive environment," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Rais S. Shaikhaidarov & Kyung Ho Kim & Jacob W. Dunstan & Ilya V. Antonov & Sven Linzen & Mario Ziegler & Dmitry S. Golubev & Vladimir N. Antonov & Evgeni V. Il’ichev & Oleg V. Astafiev, 2022. "Quantized current steps due to the a.c. coherent quantum phase-slip effect," Nature, Nature, vol. 608(7921), pages 45-49, August.
    4. S. Jezouin & M. Albert & F. D. Parmentier & A. Anthore & U. Gennser & A. Cavanna & I. Safi & F. Pierre, 2013. "Tomonaga–Luttinger physics in electronic quantum circuits," Nature Communications, Nature, vol. 4(1), pages 1-8, June.
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