We study the effects of thermal noise on the microwave-induced steps of a current-driven Josephson junction using the resistively shunted junction model for the junction. We generalize Stephen's method for calculating the width of the steps to the case of an underdamped junction, and to the case of a subharmonic step, provided that there is no overlapping of different steps. In order to treat the case of overlapping steps we introduce a new approach which enables us to calculate the distribution of fluctuations about as well as the transition rates out of the steps. All our results are usually in the form of explicit analytical expressions that facilitate a comparison with experiments.
Calibrated measurements of both the real and imaginary parts of the microwave impedance of proximity coupled superconducting weak links have been made. The measurements were compared with analytic calculations based on several different models for the supercurrent Is and quasiparticle current. For dc bias currents I1 less than the critical current Ic, the experimental results are consistent with the Josephson relation Is=Ic sinφ, where φ is the quantum phase angle. However, for I1≳Ic, the Fourier component of Is at the Josephson frequency is found to be significantly less (∼0.65±0.1) than would be predicted from Is=Ic sinφ, and consistent with Tinkham’s analysis of a phase slip process. The experimental results indicate that the phase-dependent part of the quasiparticle current, if it exists at all, is no more than 10% of the total quasiparticle current. These results do not necessarily contradict previous measurements made on true tunnel junctions because of the fundamental differences between the two types of devices.
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
fJ=2eVJ/h, related to the average transistor voltage
VJ, and Bloch oscillations of frequency
fB=IB/2e, related to the average current
IB 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.,
fJ=fB. This leads to the formation of a current step on the current-voltage curve at
IB=2efJ, 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
IB/VJ takes the fundamental value of
1/RQ, where
RQ=h/4e2 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.