Conventional Josephson Junctions Research Articles

Evidence for π-Shifted Cooper Quartets and Few-Mode Transport in PbTe Nanowire Three-Terminal Josephson Junctions.

Josephson junctions are typically characterized by a single phase difference across two superconductors. This conventional two-terminal Josephson junction can be generalized to a multiterminal device where the Josephson energy contains terms with contributions from multiple independent phase variables. Such multiterminal Josephson junctions (MTJJs) are being considered as platforms for engineering effective Hamiltonians with nontrivial topologies, such as Weyl crossings and higher-order Chern numbers. These prospects rely on the ability to create MTJJs with nonclassical multiterminal couplings in which only a few quantum modes are populated. Here, we demonstrate these requirements in a three-terminal Josephson junction fabricated on selective-area-grown (SAG) PbTe nanowires. We observe signatures of a π-shifted Josephson effect, consistent with interterminal couplings mediated by four-particle quantum states called Cooper quartets. We further observe a supercurrent coexistent with a non-monotonic evolution of the conductance with gate voltage, indicating transport mediated by a few quantum modes in both two- and three-terminal devices.

Monolithic integrated superconducting nanowire digital encoder

Superconducting digital circuits are promising technologies that can overcome bottlenecks in both classical and quantum computation due to their ultra-high operation speed and extremely low power dissipation. Superconducting nanowire cryotrons (nTrons) are emerging as one type of superconductor switching devices, offering advantages complementary to conventional Josephson junctions. Achieving monolithic integration of a reasonable number of nTrons into a functional digital circuit is a crucial step to extend its application. In this study, we constructed a monolithic integrated nTron-based binary encoder, which includes input fanout circuits, on-chip biasing, combinational logic routing and multi-gate nTrons. This represents a monolithic nTron digital circuit comprising 137 nTron gates, 424 resistors, 274 inductors, and 164 vias developed using a two-superconducting-layer fabrication process. The performance of this monolithic nTron encoder surpasses that of our previously demonstrated circuit with discrete nTron components. The maximum bias margin is 28% for the fanout circuit and 60% for the multi-gate nTron when using a signal generator, while the minimum timing jitter is 40 ps. The total power dissipation mainly from biasing resistors is 19.6 μW, making it more power efficient than RSFQ encoders. The encoder is then packaged and connected with a superconducting nanowire single-photon detector array for demonstrating its function of addressing pixel locations. Compared to the conventional readout, the nTron encoder shows a minimum readout error rate lower than 10−4 and reduces the readout RF lines from 15 to 4. The design and fabrication technologies could enrich integrated nTron digital circuits beyond current limits and promote their applications in classical and quantum systems.

NbN-based half-flux-quantum element for integration with superconducting qubits

Half-flux-quantum (HFQ) logic is a superconductor logic family comprising conventional Josephson junctions (0-JJs) and π Josephson junctions (π-JJs). The energy scale of HFQ logic can be flexibly reduced by phase shifts owing to π-JJs; thus, HFQ circuits are a promising building block for qubit interface circuits. In this study, we demonstrate an NbN-based HFQ circuit element compatible with NbN-based superconducting qubits for all-NbN monolithic integration of qubits and HFQ circuits. The use of NbN is beneficial for both qubits and HFQ circuits owing to its high-quality junctions and high kinetic inductance. First, we developed a prototype of an NbN-based 0-JJ/π-JJ hybrid fabrication process for designing HFQ circuits. We evaluated 0-JJs and π-JJs fabricated through the hybrid process, which demonstrated that the 0-JJs had a small deviation with regard to critical current density and the π-JJs had a sufficiently high critical current density to work as π phase shifters. Furthermore, we fabricated an HFQ superconducting quantum interference device, which is one of the most fundamental elements in HFQ circuits, and observed clear HFQ-period modulation in the magnetic flux dependence of the maximum current at 4.2 K.

Superconducting Quantum Circuits Based on 2D Materials

Transmon-type superconducting qubits have become a popular platform for quantum computing due to their robust qubit coherence properties. In recent years, different types of materials have been searched to replace the Al2O3 tunnel barrier in conventional Al-based Josephson junctions, in order to explore new functions of qubits utilizing the distinct nature of the chosen materials. In this report, we introduce our works involving using Weyl semimetals and graphene as a component in Josephson junctions for qubit designs and coupling to coplanar waveguide (CPW) resonators. We fabricate a MoTe2 transmon and investigate whether it exhibits topological properties by tuning the resonator frequency with magnetic flux. Next, we introduce a graphene gatemon, in which the gate-tunability of resonator frequency has been demonstrated and the two-tone spectroscopy has shown a qubit state transition.

Optimization of Half-Flux-Quantum Circuits Composed of π-Shift and Conventional Josephson Junctions

We report optimization of half-flux-quantum (HFQ) circuits composed of SQUIDs containing conventional Josephson junctions and π-shift magnetic Josephson junctions. The SQUID can act as a Josephson junction with an extremely small critical current and be easily switched by a weak driving force with the assistance of the circulating current that is induced due to the π-shift and quantization conditions. It leads to a drastic reduction of both static and dynamic power consumption. However, the parameter margins of the HFQ circuits obtained so far is narrow compared with conventional single-flux-quantum circuits. Since HFQ circuits use many circuit elements and require the two junctions in the SQUID to switch alternately and symmetrically, circuit parameter optimization is much more difficult. In this study, we developed an optimization tool for HFQ circuits, including operation judgment and margin calculation. We improved the critical margin of the HFQ Josephson transmission line to 39%. We also optimized the HFQ splitter, confluence buffer, and D flip-flop. We discuss design guidelines for HFQ circuits based on our systematic exploration of the optimized circuit parameter sets. We suggest that the optimized loop inductances are around 0.5 and 1.5 of Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /2 for data transmission and storage, respectively.

Analysis of the Effect of 0-π SQUIDs for Enhancing Mutual Coupling

This study shows that we can obtain an enhanced mutual coupling by using a superconducting quantum interference device (SQUID) containing a π-phase shift Josephson junction (π-junction). The π-junction can increase the current flowing in the loop inductance of the SQUID, thereby enhancing the magnetic flux generated in the inductance. Therefore, the effective self-inductance of the SQUID can increase, resulting in an increase in the mutual coupling. We use a 0-π SQUID formed by a conventional Josephson junction (0-junction) and a π-junction. Our numerical analysis for a simplified structure revealed that the ratio of effective to original self-inductance increased to 50. To confirm this, we measured the modulation patterns of critical current in dc-SQUIDs in which part of the loop inductance was replaced with a series of 0-π SQUIDs. The observed modulation pattern revealed that the effective self-inductance became more than 10-fold larger than the original self-inductance under the conditions that the applied current is a few μA while the critical current of the 0-junction in 0-π SQUIDs is 35 μA.

Long Single Au Nanowires in Nb/Au/Nb Josephson Junctions: Implications for Superconducting Microelectronics

The application of nanowires in superconducting electronic circuits is a prospective way to miniaturize conventional planar Josephson junctions. However, knowledge about nanowire-based devices’ fabrication technology and their performance at low temperatures is still scarce. Here, we propose a technique for obtaining long single Au nanowires and hybrid Josephson junctions formed by coupling the nanowires to planar Nb electrodes. The prospects for using electrodeposited Au nanowires with 30 and 60 nm diameters in superconducting microelectronics are illustrated by quantitative measurements of device current–voltage characteristics with weak link lengths varying from 280 to 520 nm at temperatures down to 1.2 K. The relationship between the nanowire structure and the electron transport properties of corresponding superconducting junctions is discussed. High critical current densities of Nb/Au-nanowire/Nb systems up to 1.6·106 A/cm2 combined with long-term stability make them promising candidates for the use in nanowire-based superconducting hybrid devices such as compact SQUIDs and superconducting neural networks with high integration density of circuits.

Demonstration of a superconducting diode-with-memory, operational at zero magnetic field with switchable nonreciprocity

Diode is one of the basic electronic components. It has a nonreciprocal current response, associated with a broken space/time reversal symmetry. Here we demonstrate prototypes of superconducting diodes operational at zero magnetic field. They are based on conventional niobium planar Josephson junctions, in which space/time symmetry is broken by a combination of self-field effect from nonuniform bias and stray fields from a trapped Abrikosov vortex. We demonstrate that nonreciprocity of critical current in such diodes can reach an order of magnitude and rectification efficiency can exceed 70%. Furthermore, we can easily change the diode polarity and switch nonreciprocity on/off by changing the bias configuration and by trapping/removing of a vortex. This facilitates a memory functionality. We argue that such a diode-with-memory can be used for a future generation of in-memory superconducting computers.

Fluxons in high-impedance long Josephson junctions

The dynamics of fluxons in long Josephson junctions is a well-known example of soliton physics and allows for studying highly nonlinear relativistic electrodynamics on a microscopic scale. Such fluxons are supercurrent vortices that can be accelerated by bias current up to the Swihart velocity, which is the characteristic velocity of electromagnetic waves in the junction. We experimentally demonstrate slowing down relativistic fluxons in Josephson junctions whose bulk superconducting electrodes are replaced by thin films of a high kinetic inductance superconductor. Here, the amount of magnetic flux carried by each supercurrent vortex is significantly smaller than the magnetic flux quantum Φ0. Our data show that the Swihart velocity is reduced by about one order of magnitude compared to conventional long Josephson junctions. At the same time, the characteristic impedance is increased by an order of magnitude, which makes these junctions suitable for a variety of applications in superconducting electronics.

Miniaturizing Transmon Qubits Using van der Waals Materials

Quantum computers can potentially achieve an exponential speedup versus classical computers on certain computational tasks, recently demonstrated in superconducting qubit processors. However, the capacitor electrodes that comprise these qubits must be large in order to avoid lossy dielectrics. This tactic hinders scaling by increasing parasitic coupling among circuit components, degrading individual qubit addressability, and limiting the spatial density of qubits. Here, we take advantage of the unique properties of van der Waals (vdW) materials to reduce the qubit area by >1000 times while preserving the capacitance while maintaining quantum coherence. Our qubits combine conventional aluminum-based Josephson junctions with parallel-plate capacitors composed of crystalline layers of superconducting niobium diselenide and insulating hexagonal boron nitride. We measure a vdW transmon T1 relaxation time of 1.06 μs, demonstrating a path to achieve high-qubit-density quantum processors with long coherence times, and the broad utility of layered heterostructures in low-loss, high-coherence quantum devices.

Critical currents in conventional Josephson junctions with grain boundaries

It has been hypothesized that the variation of the critical currents in Nb/Al–AlOx/Nb junctions is due to, among other effects, the presence of grain boundaries in the system. Motivated by this, we examine the effect of grain boundaries on the critical current of a Josephson junction. We assume that the hopping amplitudes are dependent on the interatomic distance and derive a physically realistic model of distance-dependent hopping amplitudes. We find that the presence of a grain boundary and associated disorder is responsible for a very large drop in the critical current relative to a clean system. We also find that when a tunnel barrier is present, grain boundaries cause substantial variations in the critical currents due to the disordered hoppings near the tunnel barrier. We discuss the applicability of these results to Josephson junctions presently intended for use in superconducting electronics applications.

Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate

Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminum-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlOx/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of ~5.2 meV for NbN, compared to ~0.3 meV for aluminum, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time {T}_{1}=16.3;{{upmu }}{{{{{rm{s}}}}}} and a spin-echo dephasing time {T}_{2}=21.5;{{upmu }}{{{{{rm{s}}}}}}. These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to the previously reported {T}_{1}approx {T}_{2}approx 0.5;{{upmu }}{{{{{rm{s}}}}}} of NbN-based qubits on MgO substrates. These results are an important step towards constructing a new platform for superconducting quantum hardware.

Demonstration of Interface Circuits Between Half- and Single- Flux- Quantum Circuits

We demonstrated interface circuits between a half-flux-quantum (HFQ) circuit and a rapid single-flux-quantum (RSFQ) circuit to obtain SFQ/HFQ and HFQ/SFQ converters. These converters were created by simply inserting a resistor between an RSFQ circuit and the adjacent HFQ circuit, where both circuits are based on pulse logic. These converters enable us to create combinatory circuits that make the best use of the features of the two circuits. Using a DC/SFQ, SFQ/HFQ, HFQ/SFQ, and SFQ/DC converter, we measure an HFQ Josephson transmission line (JTL) composed of eight 0-0-π superconducting quantum interference devices (SQUIDs), which are the essential elements of an HFQ circuit. The 0-0-π SQUIDs are composed of two conventional Josephson junctions and a π-shifted ferromagnetic junction. The HFQ JTL demonstrated in this study is driven by a bias current 11-fold lower than that of a similar RSFQ JTL. These experimental results indicate that the HFQ circuit requires power that is two or more orders of magnitude lower than that of an RSFQ circuit.

Environment-induced overheating phenomena in Au-nanowire based Josephson junctions

Unlike conventional planar Josephson junctions, nanowire-based devices have a bridge geometry with a peculiar coupling to environment that can favor non-equilibrium electronic phenomena. Here we measure the influence of the electron bath overheating on critical current of several bridge-like junctions built on a single Au-nanowire. Using the Usadel theory and applying the two-fluid description for the normal and superconducting components of the flowing currents, we reveal and explain the mutual influence of the neighbouring junctions on their characteristics through various processes of the electron gas overheating. Our results provide additional ways to control nanowire-based superconducting devices.

Anomalous Josephson effect and quantum anomaly in inversion asymmetric Weyl semimetals

We study a Josephson junction involving an inversion-asymmetric Weyl semimetal in presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0$-$\pi$ transition and a zero bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC) and TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry broken and $\mathbb{Z}_2$ symmetry broken by the respective tilt. We obtain the reversal of a pure VJC and pure CJC even in the zero bias condition controllable by the junction length. Our analysis of controllability of valley and chirality dependent transport in an inversion asymmetric Weyl semimetal junction could allow applications in valleytronics and chiralitytronics, respectively. The tilt induced Josephson effect provides an alternative route for supercurrent $0$-$\pi$ transition, different from the conventional ferromagnetism Josephson junctions where the spin polarization is essential. In the long junction and zero temperature limit, VJC and CJC are associated with a quantum anomaly which is manifested through a discontinuous jump in the current in absence of TRS and TRS breaking tilts, respectively.

High-Speed Memory Driven by SFQ Pulses Based on 0-π SQUID

We propose a new cryogenic high-speed and low-power matrix memory required for achieving a high-performance superconductor computing system. The memory cell is based on the 0-π SQUID with conventional Josephson junctions (0-junctions) and a π-shifted ferromagnetic Josephson junction (π-junction). The memory state is stored in the form of two stable states in the 0-π SQUID. The π shift feature of the π-junction eliminates the need for any bias current or magnetic field for the formation of two states, i.e., the memory is non-volatile. In this memory, an impulse-shaped voltage signal generated in single-flux-quantum (SFQ) circuits is used for the write and read operations of the memory state. By using the pulses propagating in passive transmission lines, high-speed and low-power operation can be achieved because a recharging process determining the operation speed and the dominant energy consumption can be eliminated. We fabricated the 0-π SQUID-based pulse-driven memory cells with an SFQ driver. From the static characteristics, we confirmed that the current needed for rewriting can be sufficiently reduced. In addition, we successfully demonstrated the correct write operation in the memory cell by the SFQ pulse train transmitted from the SFQ driver via the passive transmission line.

Low-power high-speed half-flux-quantum circuits driven by low bias voltages

Half-flux-quantum (HFQ) circuits store and propagate half-flux quanta. The basic circuit element is a 0-π SQUID, which is a superconducting quantum interference device with a conventional Josephson junction (0-junction) and a π-shifted ferromagnetic junction (π-junction). A 0-π SQUID achieves a small critical current in the absence of an external magnetic field, thus reducing power consumption. It is easy to set up 0-0-π SQUIDs with two 0-junctions and a π-junction which serves as a π phase-shifter. We simulated 0-0-π SQUID-based HFQ circuits driven by low bias voltages, referred to as LV-HFQ circuits. In these circuits, shunt resistors are not required for switching junctions because there is no hysteresis in the current–voltage characteristics of 0-0-π SQUIDs. We estimated the power consumption and maximum operating frequency of an HFQ Josephson transmission line based on 0-0-π SQUIDs. When operating at 43.5 GHz, the power dissipation of a single element composed of a 0-0-π SQUID and a bias resistor fell to about 0.165 nW when biased at 60 μV. The LV-HFQ circuit is potentially more power-efficient than all other currently available superconducting logic circuits.

Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons

The Josephson junctions (JJs) are at the heart of modern quantum technologies and metrology. In this work we establish quantum features of an atomic soliton Josephson junction (SJJ) device, which consists of two weakly-coupled condensates with negative scattering length. The condensates are trapped in a double-well potential and elongated in one dimension. Starting with classical field theory we map for the first time a two-soliton problem onto the effective two-mode Hamiltonian and perform a second quantization procedure. Compared to the conventional bosonic Josephson junction condensate system, we show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number, N2. A novel self-tuning effect for the effective tunneling parameter is also demonstrated in the SJJ-model, which depends on the particle number and rapidly vanishes as the JJ population imbalance increases. The formation of entangled Fock state superposition is predicted for the quantum SJJ-model, revealing dominant N00N-state components at the ‘edges’ for n = 0, N particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present in the vicinity of the major N00N-state component. This peculiarity of the quantum SJJ-model establishes an important difference from its semiclassical analogue obtained in the framework of Hartree approach. Our results are confirmed by studying the first and N-order Hillery–Zubairy criteria applied for studying multiparticle entanglement and planar spin squeezing. The Einstein–Podolsky–Rosen quantum steering represents an important prerequisite for the crossover to the mesoscopic superposition Schrödinger-cat and/or N00N-states. The feasibility in observation for these predicted states of the SJJ-model in the experiments is also discussed by taking into account one- and three-body losses for lithium condensates.

Valley supercurrent in the Kekulé graphene superlattice heterojunction

We study the possible valley supercurrent flowing in a valley Josephson junction based on the O-shaped Kekul\'e graphene superlattice (GS), in which the valley coupling term can make the valley degree of freedom condensate and open an energy gap around the Dirac point. It is found that the GS/G/GS formally resembles a conventional Josephson junction and a nonzero valley supercurrent flows through the junction when the arguments of the complex valley coupling terms in each GS are different. Unlike the conventional Josephson current, a local static potential in the middle G region via gate voltage can manipulate the valley supercurrent direction to form the 0-$\ensuremath{\pi}$ state transition and, moreover, the valley supercurrent magnitude as well as the current-phase relation can also be modulated by shifting the universal chemical potential of the system. Our findings provide a way to producing the pure valley current in the graphene system.

Energy-level quantization and single-photon control of phase slips in YBa2Cu3O7\u2013x nanowires

Significant progress has been made in superconducting quantum circuits. However new quantum devices that have longer decoherence times at higher temperatures are urgently required for quantum technologies. Superconducting nanowires with quantum phase slips are promising candidates for use in novel quantum devices. Here, we demonstrate YBa2Cu3O7-x nanowires with phase-slip dynamics and study their switching-current statistics at temperatures below 20 K. We apply theoretical models developed for Josephson junctions and show that our results provide strong evidence for energy-level quantization in the nanowires. The crossover temperature to the quantum regime of 12–13 K and the lifetime in the excited state exceeding 20 ms at 5.4 K are superior to those in conventional Josephson junctions. We also show how the absorption of a single photon changes the phase-slip and quantum state of a nanowire, which is important for the development of single-photon detectors with high operating temperature and superior temporal resolution.