Steps towards current metrology

Lukas Grünhaupt, Fabian Kaap, S. V. Lotkhov

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.

Helen S. Margolis

Rais S. Shaikhaidarov, Ilya Antonov, Kyung Ho Kim +5 more

The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.

Rais S. Shaikhaidarov, Kyung Ho Kim, Jacob Dunstan +4 more

Abstract Synchronisation of the Bloch oscillations in a small Josephson junction (JJ) under the microwave radiation leading to the current quantisation at a current equal to Cooper-pair charge × frequency × integer has been proposed as the effect dual to the Shapiro steps. Experimental confirmation of this phenomenon was delayed for a long time until last year's breakthrough when the current quantisation was demonstrated in the superconducting nanowires. The compact high impedance environment of the nanowires played a key role in the experiment. Direct observation of the current quantization in the JJs would answer the fundamental question of the Bloch oscillations and open a more feasible road for the metrological application. Here we place JJs in the high impedance environment and demonstrate dual Shapiro steps for frequencies up to 24 GHz (I=7.7 nA). The current quantisation exists, however, only in a narrow range of JJ parameters, the critical current and capacitance. We carry out a systematic study to explain this by invoking the model of the JJ in presence of the thermal noise. The findings are important for the fundamental physics and application to quantum metrology.

Andrew N. Jordan, Gerardo I. Viza, Juli 'an Mart 'Inez-Rinc 'on +3 more