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Resonant Bloch oscillations in transmons embedded in high-impedance circuits

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Superconducting circuits offers a unique setting to explore the strong-coupling counterpart to standard electrodynamics, with which a variety of quantum devices can be realized. A prerequisite for such strong coupling is a medium with very high characteristic impedance, which can be achieved by recently developed Josephson junction array transmission lines, dubbed “super-inductors”. These provide both the high impedance needed for strong quantum fluctuations, and photon modes with which to probe a quantum device, such as a small Josephson junction – i.e. a superconducting qubit. In this high-impedance environment, current through the junction is suppressed by Coulomb blockade, and is accompanied by Bloch oscillations analogous to those in crystalline systems. However, the interplay between Bloch oscillations and environmental photon resonances remains largely unexplored. In this talk I will give a brief introduction to circuit electrodynamics, superconducting qubits, and the superconductor-insulator transition. Then I will develop a model for Bloch oscillations in a transmon-type qubit placed in a high-impedance cavity [1]. The latter’s discrete spectrum will cause resonances in the voltage–current relation and the spectrum of photons radiated by the transmon. The transmon also scatters cavity photons inelastically; I will show a novel anti-Stokes-like process whereby photons gain a Bloch oscillation quantum. These signatures show how Bloch oscillations leave fingerprints across disparate energy scales. Time permitting, I will discuss how such Bloch oscillations give rise to dual-Shapiro steps, with applications to quantum metrology [2].

[1] B. Remez, V. D. Kurilovich, M. Rieger, and L. I. Glazman, Bloch Oscillations in a Transmon Embedded in a Resonant Electromagnetic Environment, arXiv:2403.04623.

[2] V. D. Kurilovich, B. Remez, and L. I. Glazman, Quantum Theory of Bloch Oscillations in a Resistively Shunted Transmon, arXiv:2403.04624.

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