Quantum theory of Bloch oscillations in a resistively shunted transmon
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929267760168960 |
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| author | Kurilovich, Vladislav D. Remez, Benjamin Glazman, Leonid I. |
| author_facet | Kurilovich, Vladislav D. Remez, Benjamin Glazman, Leonid I. |
| contents | 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, $R > R_Q = h / (2e)^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum theory of Bloch oscillations in a resistively shunted transmon Kurilovich, Vladislav D. Remez, Benjamin Glazman, Leonid I. Mesoscale and Nanoscale Physics Superconductivity 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, $R > R_Q = h / (2e)^2$. |
| title | Quantum theory of Bloch oscillations in a resistively shunted transmon |
| topic | Mesoscale and Nanoscale Physics Superconductivity |
| url | https://arxiv.org/abs/2403.04624 |