Single Josephson Junction Research Articles

Josephson diode effect in a ballistic single-channel nanowire

When time-reversal and inversion symmetry are broken, superconducting circuits may exhibit a so-called diode effect, where the critical currents for opposite directions of the current flow differ. In recent years, this effect has been observed in a multitude of systems, and the different physical ingredients that may yield such an effect are well understood. On a microscopic level, the interplay between spin–orbit coupling and a Zeeman field may give rise to a diode effect in a single Josephson junction. However, so far, there is no analytical description of the effect within a simple model. Here, we study a single-channel nanowire with Rashba spin–orbit coupling and in the presence of a Zeeman field. We show that the different Fermi velocities and spin projections of the two pseudo-spin bands lead to a diode effect. Simple analytical expressions for the diode efficiency can be obtained in limiting cases.

Multimode physics of the unimon circuit

We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to π leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method to fully account for the relevant modes and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit. Published by the American Physical Society 2024

Emergent quantum phase transition of a Josephson junction coupled to a high-impedance multimode resonator

The physics of a single Josephson junction coupled to a resistive environment is a long-standing fundamental problem at the center of an intense debate, strongly revived by the advent of superconducting platforms with high-impedance multimode resonators. Here we investigate the emergent criticality of a junction coupled to a multimode resonator when the number of modes is increased. We demonstrate how the multimode environment renormalizes the Josephson and capacitive energies of the junction so that in the thermodynamic limit the charging energy dominates when the impedance is larger than the resistance quantum and is negligible otherwise, independently from the bare ratio between the two energy scales and the compact or extended nature of the phase of the junction. Via exact diagonalization, we find that the transition surprisingly stems from a level anticrossing involving not the ground state, but the first excited state, whose energy gap vanishes in the thermodynamic limit. We clarify the nature of the two phases by pointing at a different behavior of the ground and excited states and we show that at the transition point the spectrum displays universality not only at low frequencies. In agreement with recent experiments, we reveal striking spectral signatures of the phase transition.

Phase-dependent Andreev molecules and superconducting gap closing in coherently-coupled Josephson junctions

The Josephson junction (JJ) is an essential element of superconducting (SC) devices for both fundamental and applied physics. The short-range coherent coupling of two adjacent JJs forms Andreev molecule states (AMSs), which provide a new ingredient to engineer exotic SC phenomena such as topological SC states and Andreev qubits. Here we provide tunneling spectroscopy measurements on a device consisting of two electrically controllable planar JJs sharing a single SC electrode. We discover that Andreev spectra in the coupled JJ are highly modulated from those in the single JJs and possess phase-dependent AMS features reproduced in our numerical calculation. Notably, the SC gap closing due to the AMS formation is experimentally observed. Our results help in understanding SC transport derived from the AMS and promoting the use of AMS physics to engineer topological SC states and quantum information devices.

Microwave Switch Architecture for Superconducting Integrated Circuits Using Magnetic Field-Tunable Josephson Junctions

We report on the design, fabrication, and measurement of a low-temperature microwave switch architecture that can be fully integrated on chip using single Josephson junctions and superconducting bias lines. The basic switching element used is a reflective single-pole-single-throw switch that is realized by tuning the critical current of a single Josephson junction by way of a local flux bias. A single-pole-single-throw switch is demonstrated at 4.2 K to have an on/off ratio in excess of 20 dB up to 12 GHz. This element is then incorporated into the design of a single-pole-double-throw switch that exhibits an on/off ratio above 20 dB up to 10 GHz. The switches require no intrinsic power dissipation in either state, and their performance was verified for input powers of -100 dBm to -60 dBm. S-parameter simulations using a simple lumped element model are in good agreement with the experimental data, allowing for the design to be extended to larger switch architectures.

Supercurrent in Bi4Te3 Topological Material-Based Three-Terminal Junctions

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi4Te3 and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators' weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current-phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

Stepping Closer to Pulsed Single Microwave Photon Detectors for Axions Search

Axions detection requires the ultimate sensitivity down to the single photon limit. In the microwave region this corresponds to energies in the yJ range. This extreme sensitivity has to be combined with an extremely low dark count rate, since the probability of axions conversion into microwave photons is supposed to be very low. To face this complicated task, we followed two promising approaches that both rely on the use of superconducting devices based on the Josephson effect. The first one is to use a single Josephson junction (JJ) as a switching detector (i.e. exploiting the superconducting to normal state transition in presence of microwave photons). We designed a device composed of a coplanar waveguide terminated on a current biased Josephson junction. We tested its efficiency to pulsed (pulse duration 10 ns) microwave signals, since this configuration is closer to an actual axions search experiment. We show how our device is able to reach detection capability of the order of 10 photons with frequency 8 GHz. The second approach is based on an intrinsically quantum device formed by two resonators coupled only via a superconducting qubit network (SQN). This approach relies on quantum nondemolition measurements of the resonator photons. We show that injecting RF power into the resonator, the frequency position of the resonant drop in the transmission coefficient (S21) can be modulated up to 4 MHz. We anticipate that, once optimized, both the devices have the potential to reach single photon sensitivity.

Anomalous temperature dependence of multiple Andreev reflections in a topological insulator Josephson junction

As a promising platform for unconventional superconductivity, Josephson junctions (JJs) of tetradymite topological insulators (TIs) and s-wave superconductors have been investigated in recent years. This family of TI materials, however, often suffers from spurious bulk transport, which hampers the observation of the exotic physics of their topological surface states. Thus, disentangling the transport mechanism of bulk and surface contributions in TI JJs is of high importance when investigating proximity induced superconductivity in those crystals. In this work, we add to the insights regarding these contributions by studying the temperature-dependent behaviour of a Bi2Te3-based JJ with transparent interfaces. In electrical transport measurements, we investigate differential conductance spectra of multiple Andreev reflections (MARs) and find a qualitative temperature-dependent change from peak features at low temperatures to dip features at higher ones. The observation of both kind of MAR patterns in a single JJ suggests contributions of diffusive bulk and ballistic surface states and links to a similar finding in the temperature dependence of the critical current. Our work advances the research of induced superconductivity in TIs and offers new avenues to study the induced superconductivity in the topological surface states of these materials.

Unimon qubit

Superconducting qubits seem promising for useful quantum computers, but the currently wide-spread qubit designs and techniques do not yet provide high enough performance. Here, we introduce a superconducting-qubit type, the unimon, which combines the desired properties of increased anharmonicity, full insensitivity to dc charge noise, reduced sensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator. In agreement with our quantum models, we measure the qubit frequency, ω01/(2π), and increased anharmonicity α/(2π) at the optimal operation point, yielding, for example, 99.9% and 99.8% fidelity for 13 ns single-qubit gates on two qubits with (ω01, α) = (4.49 GHz, 434 MHz) × 2π and (3.55 GHz, 744 MHz) × 2π, respectively. The energy relaxation seems to be dominated by dielectric losses. Thus, improvements of the design, materials, and gate time may promote the unimon to break the 99.99% fidelity target for efficient quantum error correction and possible useful quantum advantage with noisy systems.

Meissner effect in Fock space

By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, a synthetic gauge field is generated in the Fock space of the system. At a critical synthetic gauge flux the ground state undergoes a quantum phase transition which is analogous to the Meissner-Abrikosov-vortex transition found in type-II superconductors with an applied magnetic field. A second quantum phase transition involving attractive interactions between the bosons of the BJJ is shown to enhance the sensitivity of the system to the Meissner-Abrikosov-vortex transition.

Josephson Diode Effect in High-Mobility InSb Nanoflags.

We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. The effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin-orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the supercurrent asymmetry, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material.

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.

Flux focused series arrays of long Josephson junctions for high-dynamic range magnetic field sensing

Series arrays of closely spaced, planar long Josephson junctions were demonstrated to be transducers of magnetic flux featuring high-dynamic range, wide-bandwidth, and the capability to operate at cryogenic nitrogen temperatures. By tuning and scaling the geometry of these devices, it is possible to improve their sensitivity to an applied magnetic field and to generate higher voltage responses. Moreover, these devices feature linear voltage responses allowing for the potential of unlocked operation. Herein, we study the flux focusing effect in series arrays of planar Josephson junctions, which are well-suited to fabrication in thin films of the high-transition temperature superconductor YBa2Cu3O7−δ via helium focused ion beam irradiation. We present efforts to characterize the array geometry and properties for magnetic field sensing, with investigations of single Josephson junction behavior and demonstrations of small and large series arrays of Josephson junctions. Furthermore, two-tone spectroscopy is performed to quantify the practical linearity of the voltage response. In this work, a series array of 2640 long Josephson junctions is demonstrated, achieving a sensitivity of 1.7 mV/μT and a linear response over a region of 10.6 μT resulting in a dynamic range of 117 dB while operating at 40 K.

Phase diffusion and noise temperature of a microwave amplifier based on single unshunted Josephson junction

High-gain microwave amplifiers operating near quantum limit are crucial for development of quantum technology. However, a systematic theoretical modeling and simulations of their performance represent rather challenging tasks due to the occurrence of colored noises and nonlinearities in the underlying circuits. Here, we develop a response theory for such an amplifier whose circuit dynamics is based on nonlinear oscillations of an unshunted Josephson junction. The theory accounts for a subtle interplay between exponentially damped fluctuations around the stable limit cycle and the nonlinear dynamics of the limit cycle phase. The amplifier gain and noise spectrum are derived assuming a colored voltage noise at the circuit resistor. The derived expressions are generally applicable to any system whose limit cycle dynamics is perturbed by a colored noise and a harmonic signal. We also critically assess reliabilities of numerical methods of simulations of the corresponding nonlinear Langevin equations, where even reliable discretization schemes might introduce errors significantly affecting simulated characteristics at the peak performance.

THz microscope for three-dimensional imaging with superconducting Josephson junctions.

Superconducting Josephson junctions have a wide range of applications ranging from quantum computing to voltage standards, and they may also be employed as versatile sensors for high-frequency radiation and magnetic fields. In this work, we present a unique measurement setup utilizing a single Josephson junction on a cantilever for high-resolution spatial measurements of spectroscopically resolved THz and microwave field distributions. This THz microscope can be utilized to measure power and frequency of electromagnetic radiation from ∼1GHz to 5THz. It may also be used to measure static magnetic fields and provide topological scans of samples. The samples can be both actively radiating or passively irradiated at either room temperature or cryogenic temperatures. We review the measurement setup of the THz microscope and describe the evaluation of its measurement data to achieve three-dimensional visualizations of the field distributions. The diverse capabilities of this unique tool are demonstrated by its different measurement modes with measurements of field distributions at 20GHz and 1.4THz, spectroscopically resolved THz measurements, and magnetic field measurements.

Geometric Superinductance Qubits: Controlling Phase Delocalization across a Single Josephson Junction

There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wavefunction. In the other the junction is added in parallel, which gives rise to an extended phase variable, continuous wavefunctions and a rich energy level structure due to the loop topology. While the corresponding rf-SQUID Hamiltonian was introduced as a quadratic, quasi-1D potential approximation to describe the fluxonium qubit implemented with long Josephson junction arrays, in this work we implement it directly using a linear superinductor formed by a single uninterrupted aluminum wire. We present a large variety of qubits all stemming from the same circuit but with drastically different characteristic energy scales. This includes flux and fluxonium qubits but also the recently introduced quasi-charge qubit with strongly enhanced zero point phase fluctuations and a heavily suppressed flux dispersion. The use of a geometric inductor results in high precision of the inductive and capacitive energy as guaranteed by top-down lithography - a key ingredient for intrinsically protected superconducting qubits. The geometric fluxonium also exhibits a large magnetic dipole, which renders it an interesting new candidate for quantum sensing applications.

Vacuum-gap transmon qubits realized using flip-chip technology

Significant progress has been made in building large-scale superconducting quantum processors based on flip-chip technology. In this work, we use flip-chip technology to realize a modified transmon qubit, denoted as the “flipmon,” whose large shunt capacitor is replaced by a vacuum-gap parallel plate capacitor. We place one of the qubit pads and a single Josephson junction on the bottom chip and the other pad on the top chip, which is galvanically connected with the junction through an indium bump. The electric field energy participation ratio can arrive at nearly 53% in air when the vacuum-gap is about 5 μm, thus potentially leading to a lower dielectric loss. The coherence times of the flipmons are obtained in the range of 30–60 μs, which are comparable with that of conventional transmons with similar fabrication processes. The electric field simulation indicates that the metal-air interface's energy participation ratio increases significantly and may dominate the flipmon's decoherence. This suggests that more careful surface treatment needs to be considered. No evidence shows that the indium bumps inside the flipmons cause significant decoherence. With well-designed geometry and good surface treatment, the coherence of the flipmons can be further improved.

Josephson junction model with cosine interference term: Analysis, microcontroller implementation, and network analysis

The dynamical behavior of a single and network of Josephson junction (JJ) model with cosine interference term (CIT) is explored in this paper. The rate-equations describing a single JJ model with CIT have no or two equilibrium points as a function of direct current (DC). The stability of two equilibrium points reveals that one of the equilibrium points is stable node and other is saddle node. The presence of CIT leads to the change of regular spiking and intrinsic bursting to periodic bursting. JJ circuit model with CIT shows the existence of bistable periodic attractors, periodic attractors, hidden chaotic attractors, and coexisting attractors during the numerical simulations. By increasing the coherence parameter, the coexisting attractors are controlled to bistable limit cycles. The microcontroller implementation of the JJ model with CIT is implemented to ascertain the results of numerical simulations. To demonstrate the collective behavior of the JJ model with CIT, a lattice array of identical JJ models with CIT is constructed and studied. By considering the coupling constant as the control parameter, it is demonstrated that the existence of incoherent nodes for lower coupling values and formation of chimera states when the coupling strength is increased.

On the origin of the controversial electrostatic field effect in superconductors

Superconducting quantum devices offer numerous applications, from electrical metrology and magnetic sensing to energy-efficient high-end computing and advanced quantum information processing. The key elements of quantum circuits are (single and double) Josephson junctions controllable either by electric current or magnetic field. The voltage control, commonly used in semiconductor-based devices via the electrostatic field effect, would be far more versatile and practical. Hence, the field effect recently reported in superconducting devices may revolutionise the whole field of superconductor electronics provided it is confirmed. Here we show that the suppression of the critical current attributed to the field effect, can be explained by quasiparticle excitations in the constriction of superconducting devices. Our results demonstrate that a miniscule leakage current between the gate and the constriction of devices perfectly follows the Fowler-Nordheim model of electron field emission from a metal electrode and injects quasiparticles with energies sufficient to weaken or even suppress superconductivity.

Magnetic Field Sensor Based on a Single Josephson Junction With a Multilayer Ferromagnet/Normal Metal Barrier

We report experimental studies of quantum-matter heterostructures based on a ferromagnet/normal metal multilayer proximitized by Nb superconducting electrodes to form a novel Josephson weak-link device that is highly sensitive to magnetic fields. The device is a single Josephson junction containing Al/Ni or Al/Py (Py: Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">80</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> ) multilayer structures, which manifests quasi-sinusoidal critical current oscillations resembling the response of a dc Superconducting Quantum Interference Device (SQUID). Our analysis shows that the field sensitivity of this novel device, as measured by the magnetic field needed to form one period of the oscillations, is about twice that reported for recent micro- or nano-SQUIDs. We present an analysis of the temperature dependence of the period of the oscillations and the Josephson critical current, as well as the background current. We believe that our devices are promising candidates for a new generation of magnetic field nanosensors.