We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency $f_J=2e\overline{V_J}/h$, related to the average transistor voltage $\overline{V_J}$, and Bloch oscillations of frequency $f_B=\overline{I_B}/2e$, related to the average current $\overline{I_B}$ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., $f_J=f_B$. This leads to the formation of a current step on the current-voltage curve at $\overline{I_B}=2e{f}_J$, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency $f$ on the current-voltage curve of a small Josephson junction at current $I=2ef$. Moreover, the Bloch transistor transconductance $\overline{I_B}/\overline{V_J}$ takes the fundamental value of $1/R_Q$, where $R_Q=h/4e^2$ is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.

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• Josephson effect
• Quantum metrology
• Coupled oscillators
• Josephson junctions
• Single-electron devices
• Superconducting devices