Josephson Array Research Articles

Synthetic complex Weyl superconductors, chiral Josephson effect and synthetic half-vortices

We show that the most generic form of spin-singlet superconducting order parameter for chiral fermions in systems with broken time reversal symmetry and inversion symmetry is of the Delta _s+igamma ^5Delta _5 where Delta _s is the usual order parameter and Delta _5 is the pseudo-scalar order parameter. After factoring out the U(1) phase e^{iphi }, this form of superconductivity admits yet additional complex structure in the plane of (Delta _s,Delta _5). The polar angle chi in this plane, which we call the chiral angle, can be controlled by the external flux bias. We present a synthetic setup based on stacking of topological insulators (TIs) and superconductors (SCs). Alternatively flux biasing the superconductors with a fluxes pm Phi leads to Delta _5=Delta _0 sin (chi ), where Delta _0 is the superconducting order parameter of the SC layers, and the chiral angle chi ={2pi }Phi /Phi _0 is directly given by the flux Phi in units of the flux quantum Phi _0=h/(2e). This can be used as a building block to construct a two-dimensional Josephson array. In this setup chi will be a background field defining a pseudoscalar Delta _5 that can be tuned to desired configuration. While in a uniform background field Delta _5 the dynamics of phi is given by standard XY model and its associated vortices, a staggered background pm Delta _5 (or equivalently chi and chi +pi in alternating lattice sites) creates a new set of minima for the phi field that will support half-vortex excitations. An isolated single engineered “half-vortex” in the chi field in an otherwise uniform background will bind a phi -half-vortex. This is similar to the way a p-wave superconducting vortex core binds a Majorana fermion.

Bistability and nonequilibrium condensation in a driven-dissipative Josephson array: A c-field model

Developing theoretical models for nonequilibrium quantum systems poses significant challenges. Here we develop and study a multimode model of a driven-dissipative Josephson junction chain of atomic Bose-Einstein condensates, as realised in the experiment of Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)]. The model is based on c-field theory, a beyond-mean-field approach to Bose-Einstein condensates that incorporates fluctuations due to finite temperature and dissipation. We find the c-field model is capable of capturing all key features of the nonequilibrium phase diagram, including bistability and a critical slowing down in the lower branch of the bistable region. Our model is closely related to the so-called Lugiato-Lefever equation, and thus establishes new connections between nonequilibrium dynamics of ultracold atoms with nonlinear optics, exciton-polariton superfluids, and driven damped sine-Gordon systems.

Superconductivity from a melted insulator in Josephson junction arrays.

Arrays of Josephson junctions are governed by a competition between superconductivity and repulsive Coulomb interactions, and are expected to exhibit diverging low-temperature resistance when interactions exceed a critical level. Here we report a study of the transport and microwave response of Josephson arrays with interactions exceeding this level. Contrary to expectations, we observe that the array resistance drops dramatically as the temperature is decreased-reminiscent of superconducting behaviour-and then saturates at low temperature. Applying a magnetic field, we eventually observe a transition to a highly resistive regime. These observations can be understood within a theoretical picture that accounts for the effect of thermal fluctuations on the insulating phase. On the basis of the agreement between experiment and theory, we suggest that apparent superconductivity in our Josephson arrays arises from melting the zero-temperature insulator.

Development of an SIS Mixer-Based Low-Noise Amplifier Amenable to Josephson Oscillator Pumping

We propose a low-noise and low-power-consumption microwave amplifier using superconductor-insulator-superconductor (SIS) mixers as quasi-particle frequency up- and down-converters pumped by a Josephson array oscillator in the millimeter-wave band. A proof-of-concept study of an amplifier with two W-band waveguide mixers using Nb/Al-AlOx/Nb junctions in a cascade connection demonstrated an average gain of 6 dB and a noise temperature of 12 K from nearly DC to 5 GHz. We also designed and fabricated a Josephson array oscillator at 100 GHz, which consisted of 31 overdamped Josephson junctions placed at each half-wavelength in an Nb microstrip line. The estimated output power of the oscillator was 0.2 μW at 100 GHz, which can be increased by increasing the number of the oscillator junctions. These results suggest that the proposed SIS mixer-based amplifier is suitable for on-chip integrated circuits to be implemented in large-scale multipixel SIS receivers and quantum computers.

Designing Large Two-Dimensional Arrays of Josephson Junctions for RF Magnetic Field Detection

This paper discusses improved design of two-dimensional (2D) arrays, potentially pushing the present state of the art of the high-Tc (and low-Tc) magnetic field detectors to a larger scale, i.e., higher sensitivity. We propose a two-plate geometry for parallel (and two-dimensional) arrays of Josephson junctions (JJs) for application in magnetic field detection. The arrays can be realized either by integration in the same substrate with a multilayer technology or on two different substrates. In the latter case, the substrates can be assembled in a flip-chip or piggyback configuration. A suggestion would be to divide a 2D array in two (equal) parts and to distribute each part on a different layer, one above the other. We model the current distribution in arrays connected in series so that the bias current flowing through the device flows in opposite direction in the layers. We demonstrate that this geometry greatly improves the uniformity of the bias current distribution across the width of the array, thereby restoring the critical current and, in principle, improving the Josephson array response. From the model, we conclude that the alignment of the arrays is not critical and that the realization of the devices requires only conventional techniques.

Tidal Force Leap May Cause Malignant Impact on Zener Standard Measurement and Even Aircraft Instrumentation System

From 1996 to 1997, the National Metrology Centre of Singapore (NMC) coordinated the 3rd Asia Pacific Metrology Program (APMP) comparison of dc voltage using a Zener traveling standard. The comparison results at 1.018 V showed a zigzag curve among those laboratories that used their Josephson Array Voltage Standards (JAVSs) for this comparison. The amplitude of the zigzag was more than 1 part in 107, much larger than the typical uncertainty of such standards. These results motivated NMC to search for an explanation, which finally led to the development of an approximate mathematical model to describe this phenomenon [1]. During this developing period a surprising phenomenon was observed: Continuously measured dc voltage output with a periodic fluctuation pattern correlated with the times of tide high and tide low [2]. In addition to this, [2] also mentioned another observation that some of measurements carried out exhibit vast errors during spring tide. Through water molecules’ adsorption or desorption on the insulation of a wiring harness forming the voltage divider, which is situated in an air sealed thermostat of a measured Zener cell, the dc voltage output was very strongly disturbed by spring tides.

Synchronization on star-like graphs and emerging $\mathbb{Z}_{p}$ symmetries at strong coupling

Abstract We discuss the aspects of synchronization on inhomogeneous star-like graphs with long rays in the Kuramoto model framework. We assume the positive correlation between internal frequencies and degrees for all nodes which supports the abrupt first-order synchronization phase transition. It is found that different ingredients of the graph get synchronized at different critical couplings. Combining numerical and analytic tools, we evaluate all critical couplings for the long star graph. Surprisingly, it is found that at strong coupling there are discrete values of coupling constant that support the synchronized states with emerging $\mathbb{Z}_{p}$ symmetries. The stability of the synchronized phase is discussed, and the interpretation of the phase with emerging $\mathbb{Z}_{p}$ symmetry for the Josephson array on a long star graph is mentioned.

Intrinsically shunted NbN/TaN/NbN Josephson junctions on Si substrates for large-scale integrated circuits applications

Superconducting circuits based on Josephson junctions have the potential to achieve high speed and ultra-low power consumption, but their integration is limited by the low controllability of Nb-based tunnel junction and the existence of shunt resistors. In this work, we report the fabrication of superconductor/normal metal/superconductor (SNS) Josephson junctions with high reproducibility on oxidized Si substrates. The junctions based on NbN/TaN/NbN trilayers measured at 4.2 K show excellent Josephson properties with a wide range of critical current (I c) from 227 to 2000 μA. The variations of critical current density (J c) and characteristic voltage (V c) are respectively less than 7.1% and 7.5% in the 2 inch region. The standard deviation of I c is calculated to be less than 1.7% for Josephson arrays with the number of junctions up to 10 000 occupying an area of 0.34 mm2. The results provide a guarantee for the applications of NbN-SNS Josephson junctions in superconducting large-scale integrated circuits.

Comparison of the Josephson voltage standards of the MIKES and the BIPM

Main textAs part of the ongoing BIPM key comparison BIPM.EM-K10.b, a direct comparison of the Josephson array voltage standards of the Bureau International des Poids et Mesures (BIPM) and the National Metrology Institute of Finland (VTT MIKES), Espoo, Finland, was carried out in October 2019 at the level of 10 V. For this exercise, the option A of the BIPM.EM-K10.b comparison protocol was partially applied. Option A required the MIKES to provide a reference voltage with its Josephson voltage standard for measurement by the BIPM using an analogue nanovoltmeter and associated measurement cables. Since no sufficiently stable voltage could be achieved in this configuration, a digital detector was used instead. In all cases the BIPM array was kept floating from ground.The final results were in good agreement within the combined relative standard uncertainty of 2.5 parts in 1010 for the nominal voltage of 10 V.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database https://www.bipm.org/kcdb/.The final report has been peer-reviewed and approved for publication by the CCEM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Superconductor-like effects in an ac-driven normal Mott-insulating quantum dot array

We study the current response of an AC driven dissipative Mott insulator system, a normal quantum dot array, using an analytical Keldysh field theory approach. Deep in the Mott insulator regime, the nonequilibrium steady state (NESS) response resembles a resistively shunted Josephson array, with a nonequilibrium Mott insulating to conductor transition as the drive frequency {\Omega} is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the {\eta}-pairing phase of a Josephson array with negative phase stiffness. However in the presence of an additional DC field the signature of supercurrent - Shapiro steps - is completely absent. We interpret these properties as number-phase fluctuation effects shared with Josephson systems rather than superconductivity.

Measurement and analysis of high-frequency voltage errors in the Josephson arbitrary waveform synthesizer

This paper reports on the comparison of two Josephson arbitrary waveform synthesizers for frequencies up to 500 kHz. Both independent pulse-driven Josephson arrays produce a 10 mV RMS sinusoidal voltage. They are alternately connected to an analog-to-digital converter which serves as a transfer standard. The setup is capable to of synthesizing quantum-based waveforms using two different pulse-bias techniques. We use the Zero-Compensation method and a two-pole high-pass filter structure in the pulse-bias configuration of one system (the reference) to minimize the amplitude error for signal frequencies up to 500 kHz. Consequently, we are able to directly detect the high-frequency voltage errors in the other system (the device under test). The setup is used to measure differences between both systems, and the influence of parameter variation on the results with Type A uncertainties of 0.4 µV/V (k = 1) in measurement times of 60 s. We find that the dominant sources of deviations above 10 kHz can be traced to the influence of the output cabling and the pulse bias on the synthesized voltage signal. Our analysis explains the origin and the reduction of these high-frequency voltage errors.

Josephson Array-Mode Parametric Amplifier

We introduce a novel near-quantum-limited amplifier with a large tunable bandwidth and high dynamic range - the Josephson Array Mode Parametric Amplifier (JAMPA). The signal and idler modes involved in the amplification process are realized by the array modes of a chain of 1000 flux tunable, Josephson-junction-based, nonlinear elements. The frequency spacing between array modes is comparable to the flux tunability of the modes, ensuring that any desired frequency can be occupied by a resonant mode, which can further be pumped to produce high gain. We experimentally demonstrate that the device can be operated as a nearly quantum-limited parametric amplifier with 20 dB of gain at almost any frequency within (4-12) GHz band. On average, it has a 3 dB bandwidth of 11 MHz and input 1 dB compression power of -108 dBm, which can go as high as -93 dBm. We envision the application of such a device to the time- and frequency-multiplexed readout of multiple qubits, as well as to the generation of continuous-variable cluster states.

Microwave Modeling and Characterization of Superconductive Circuits for Quantum Voltage Standard Applications at 4 K

In this article, we characterize the microwave behavior of superconductive circuits for quantum voltage standard applications at 4 K. For that, we develop a cryogenic multiline thru-reflect-line (TRL) calibration procedure to calibrate the microwave measurements at the 4 K on-wafer reference plane. We model superconductive circuits, including a Josephson array transmission line, compare simulated to TRL-calibrated measured results, and find excellent agreement up to 50 GHz.

Pulsation of InGaAs Photodiodes in Liquid Helium for Driving Josephson Arrays in AC Voltage Realization

A commercially available InGaAs p-i-n photodiode chip has been custom packaged and high-speed operated in liquid helium. The photodiode was driven by light pulses using a dc-biased 1310-nm laser, a Mach-Zehnder modulator, and a return-to-zero pulse pattern generator up to 15 GHz clock frequencies, which produced pulse widths down to 77 ps and maximum peak current heights above 10 mA. With the prospect of using this photodiode assembly to operate pulse-driven Josephson junction arrays for ac voltage realization, pulsation modes with constant pulse width and varying pulse density were applied to the diode, which resulted in consistent pulse shapes for bit rates as high as 7.5 Gb/s. This could yield realizable peak voltages as high as 15.525 μV per Josephson junction. Time-lapse pulse measurements were performed over the span of 90 min, which demonstrated good waveform stability. Using the measured current waveforms, the behavior of a typical Josephson junction was simulated according to the Stewart-McCumber model, which resulted in an operational margin of 2 mA for the first Shapiro step.

1 GHz Waveform Synthesis with Josephson Arrays

1 GHz Waveform Synthesis with Josephson Arrays

Superconductivity in an insulator

The superconductor–insulator phase transition is a quantum phenomenon that reveals a competition between the superconducting phase order and charge localization. Now, microwave spectroscopy is shown to be a promising approach to investigate this effect in controllable one-dimensional Josephson arrays.

Voltage Standard Based on Dry-Cooled High-Temperature Superconductor Josephson Junctions

A commercially available compact Josephson voltage standard N4-21 based on high-temperature superconductor Josephson junctions with dry nitrogen temperature cooling is presented. The cryocooler unit of the voltage standard including the cryogenic system and the high-temperature superconductivity Josephson array chip is described. The measured relative standard uncertainties between output voltages of N4-21 and the primary state voltage standard of Russia are only a few parts in 108. Such low uncertainties are sufficient for the application of voltage standard N4-21 in the highest-level metrology. The implementation of the link between Josephson junctions and Zener diodes largely eliminates the uncertainty contributions associated with Zeners nonlinear drift, environmental effects, and the impact due to shipping.

Non-Conventional PJVS Exploiting First and Second Steps to Reduce Junctions and Bias Lines

Quantum digital-to-analog converters (DACs) based on programmable Josephson array [Programmable Josephson Voltage Standard (PJVS)] represent the most widely used quantum standard in ac voltage calibrations. The extension of PJVS frequency above the kilohertz range appears to be arduous; however, some enhancements are still practicable. In this work, we demonstrate the possibility to advantageously operate a conventional binary-divided PJVS array with a reduced number of bias lines. This feature is achieved by exploiting both the first and the second Shapiro steps along with nonconventional DAC codings. Two newly devised bias techniques are described in detail and preliminary experimental tests on waveform synthesis have been carried out and are presented here.

Development of 0.5-V Josephson junction array devices for quantum voltage standards**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFF02000402).

The design, fabrication, and the characterization of a 0.5-V Josephson junction array device are presented for the quantum voltage standards in the National Institute of Metrology (NIM) of China. The device consists of four junction arrays, each of which has 1200 3-stacked Nb/NbxSi1−x/Nb junctions and an on-chip superconducting microwave circuit which is mainly a power divider enabling each Josephson array being loaded with an equal amount of microwave power. A direct current (dc) quantum voltage of about 0.5 V with a ∼1-mA current margin of the 1st quantum voltage step is obtained. To further prove the quality of NIM device, a comparison between the NIM device with the National Institute of Standards and Technology (NIST) programmable Josephson voltage standard (PJVS) system device is conducted. The difference of the reproduced 0.5-V quantum voltage between the two devices is about 0.55 nV, which indicates good agreement between the two devices. With the homemade device, we have realized a precise and applicable 0.5-V applicable-level quantum voltage.

Integration density of ion-damaged barrier Josephson junction and circuits

We investigate on the integration density limit of the superconducting technology for Josephson devices and circuits based on ion-damaged barrier. This technology is suitable for very large integration of superconducting circuits as the footprint of the Josephson junction is of the order of 40 nm by 2 μm. Series arrays of Josephson junction can be designed for high voltage amplitude at the device terminals.We have fabricated single Josephson junctions and arrays of 2 and/or 10 Josephson junctions connected in series with equal spacing. This spacing was varied on different devices from 100 nm to 1.6 μm. We observe a strong change in the parameters characterizing the DC transport in the arrays with the highest density of the Josephson junctions. It shows that the scaling behavior of Josephson array DC properties strongly depends on the distance separating 2 consecutive Josephson junctions. We discuss the origin of these effects presumably due to defects created at long distance during the ion irradiation process. Comparison of magnetic field responses for an array and single Josephson junctions shows a reduction of the Meissner effect in the array.