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Quantum theory of Bloch oscillations in a resistively shunted transmon
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Quantum theory of Bloch oscillations in a resistively shunted transmon
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Paper
Quantum theory of Bloch oscillations in a resistively shunted transmon
2024
Overview
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 broad-band. 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 > R_Q = h / (2e)^2\\).
Publisher
Cornell University Library, arXiv.org
