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.
We have studied experimentally the current-voltage characteristics of double-barrier Nb-Al-AlO/sub x/-Al-AlO/sub x/-(Al-)Nb junctions exposed to microwave radiation at 4.2 K. Both integer and fractional Shapiro steps were observed. A complicated behavior of the step heights was observed as a function of both the microwave power and an applied magnetic field. Reasonable agreement with the RSJ model was obtained only for the steps 0 to 2 observed in current-voltage characteristics of the junctions with a "clean" middle Al layer. A deviation from RSJ-like behavior was found for higher-order integer steps and fractional steps. Devices with a "dirty" middle Al layer displayed more significant deviation from RSJ-like behavior. Step heights vs. magnetic field dependences in some cases were found to be qualitatively different from the field dependence of the dc Josephson current.
With a thin gold layer, we fabricated mesa-like shunted intrinsic Josephson junction stacks on Bi2Sr2CaCu2O8+x single crystals. Instead of the multibranch structure and large voltage jumps often observed in conventional intrinsic junctions, current–voltage characteristics typical of resistively shunted junctions were obtained. Individual Shapiro steps were clearly visible with irradiation at frequencies from a few to 20 GHz. The experiments demonstrated not only the ac Josephson effects directly but also the possibility of employing intrinsic Josephson junctions in high-frequency applications.
Microwave-induced steps were observed in I-V characteristics of intrinsic Josephson junctions fabricated on an overdoped BSCCO single crystal with a weak magnetic field parallel to the c-axis. Voltage intervals between the steps under the irradiation of 12.2, 13.2 and 13.9 GHz microwaves were independent of the microwave power and proportional to the frequency. From the measurement of voltage intervals, it was found that all the junctions in the fabricated junction stack simultaneously produced Shapiro steps, assuming that the steps are Shapiro steps.
We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ${\ensuremath{\omega}}_{\mathrm{mw}}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}$ in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the $I\text{\ensuremath{-}}V$ characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.
Electrical quantum metrology using superconducting circuits relies on phase synchronization effects of Josephson oscillations with ac signals, resulting in equidistant voltage steps and forming the basis of today’s voltage standards. Because charge and phase are conjugate variables, the dual effect of equidistant current steps should also exist and was indeed predicted theoretically. It relies on so-called Bloch oscillations, which are oscillations of voltage occurring when a current-biased Josephson junction is embedded in an environment with characteristic impedance larger than the superconducting resistance quantum h/4e^2. In addition, Josephson junctions of lateral size on the order of tens of nm are necessary, such that their Josephson and charging energy are approximately equal. Synchronizing such Bloch-oscillations with an ac signal completes the duality with Shapiro steps, and results in the occurrence of steps in IV-measurements at I=2ef with e being the elementary charge, and f the frequency of the external ac signal. To emphasize the duality with Shapiro (voltage) steps, such current steps are called dual-Shapiro steps. Together with the established standards for voltage and resistance, a new standard for current based on dual-Shapiro steps would relate the ampere, volt and ohm through fundamental constants and frequency. If successfully realized with metrological precision this would close the quantum metrological triangle and might even enable the combination of all three electric quantum relations in one single device. Here we show our efforts towards the realization of quantized currents with metrological applicability. Based on advances in fabrication technology and measurement capabilities, we demonstrate quantized current steps up to I≈2 nA by synchronizing Bloch oscillations with external ac signals up to 6 GHz [1,2]. In addition, we demonstrate a pulsed driving scheme resulting in an asymmetric pattern of dual-Shapiro steps featuring increased differential resistance [2]. Finally, we discuss the effects limiting the precision of our quantized current steps and present our efforts for tackling them. [1] F. Kaap et al., “Synchronization of Bloch Oscillations in a Strongly Coupled Pair of Small Josephson Junctions: Evidence for a Shapiro-like Current Step,“ Phys. Rev. Lett. 132, 027001, 2024. [2] F. Kaap et al., “Demonstration of dual Shapiro steps in small Josephson junctions,“ Nature Communications 15, 8726, 2024.