Josephson Junction Arrays Research Articles

Topological transitions in the presence of random magnetic domains

The Berezinskii-Kosterlitz-Thouless (BKT) transition is a topological transition driven by topological defects at a characteristic temperature, below which vortex-antivortex pairs bound and dissociate into free vortices above. Such transitions have been observed in superfluid helium films, superconducting films, quantum Hall systems, planar Josephson junction arrays, graphene, and frustrated magnets. Here we report the BKT-like transition in a quantum anomalous Hall insulator film. This system is a 2D ferromagnet with broken time-reversal symmetry, which results in quantized chiral/antichiral edge states around the boundaries of the magnetic domains/antidomains. The bindings and unbindings of these domain-antidomain pairs can take the roles played by vortex-antivortex pairs while the chirality takes over the vorticity, which drive the system to undergo the BKT-like transition. This multidomain network can be manipulated by coherent/competitive mechanisms like the applied dc current, perpendicular magnetic field, and temperature, the combination of which forms a line of critical points.

Braiding Operations for a Topological Josephson Junction Array using SFQ Current Pulses

Majorana bound states (MBSs) can occur in topological Josephson junction (JJ) arrays with the presence of a fractional vortex with 2π-phase winding. It has been theoretically shown that the braiding operation can be achieved by using current pulses, compatible with single flux quantum (SFQ) technology. Therefore, we designed an SFQ logic circuit for the braiding operations of the topological JJ array using single flux quanta in a conventional JJ array. Braiding operations could be realized by an SFQ logic circuit with double flux quantum driver. To obtain positive and negative current pulses using the SFQ logic circuit, we used SFQ logic circuits with ac biasing for simulation. Finally, we confirmed the CNOT operation using an array-type SFQ circuit by means of simulation and estimated the CNOT operation speed.

Weak ergodicity breaking in Josephson-junction arrays

We study the quantum dynamics of Josephson-junction arrays. We find isolated groups of low-entanglement eigenstates that persist even when the Josephson interaction is strong enough to destroy the overall organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates lie in the inner part of the spectrum, far from the spectral edge, and provide a weak ergodicity breaking, reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity probes, we find that the system tends toward more ergodicity for increasing system size: The parameter range where the bulk of the eigenstates look nonergodic shrinks for increasing system size. We study two geometries, a one-dimensional chain and a two-leg ladder. In the latter case, adding a magnetic flux makes the system more ergodic.

In situ Tuning of the Electric-Dipole Strength of a Double-Dot Charge Qubit: Charge-Noise Protection and Ultrastrong Coupling

Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology. Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to high-impedance superconducting quantum interference device array and Josephson-junction array resonators. We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates. We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations. We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence rates Γ2/2π<5 MHz in the limit of high interdot capacitance. In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator. Employing a Josephson-junction array resonator with an impedance of approximately 4 kΩ and a resonance frequency of ωr/2π∼5.6 GHz, we observe a coupling strength of g/2π∼630 MHz, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC). The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.6 MoreReceived 26 October 2021Revised 3 April 2022Accepted 26 May 2022DOI:https://doi.org/10.1103/PhysRevX.12.031004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information architectures & platformsQuantum information processingQuantum information with hybrid systemsQuantum information with solid state qubitsQuantum Information

Development of Quantum Limited Superconducting Amplifiers for Advanced Detection

Ultralow-noise microwave amplification and detection play a central role in different applications, going from fundamental physics experiments to the deployment of quantum technologies. In many applications the necessity of reading multiple detectors, or cavities or qubits, calls for large bandwidth amplifiers with the lowest possible noise. Current technologies are based on High Electron Mobility Transistors and Josephson Parametric Amplifiers. Both have limitations, the former in terms of the minimum noise, the latter in terms of bandwidth. Superconducting Traveling Wave Parametric Amplifiers (TWPAs) have the potential of offering quantum limited noise and large bandwidth. These amplifiers are based on the parametric amplification of microwaves traveling along a transmission line with embedded nonlinear elements. We are developing superconducting TWPAs based both on Josephson junction arrays (Traveling Wave Josephson Parametric Amplifiers) and on nonlinear kinetic inductance (Dispersion Engineered Traveling Wave Kinetic Inductance Amplifiers). Our goal is to achieve large bandwidth (in the 5 to 10 GHz range), large gain (more than 20 dB), large saturation power (more than −50 dBm), and near quantum limited noise (noise temperature less than 600 mK). Current achievements in the design and development of the high performance TWPAs are here reported and discussed, together with current limitations and possible future developments.

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.

Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase

A general framework is proposed to solve the two-dimensional fully frustrated XY model for the Josephson junction arrays in a perpendicular magnetic field. The essential idea is to encode the ground-state local rules induced by frustrations in the local tensors of the partition function. The partition function is then expressed in terms of a product of one-dimensional transfer matrix operator, whose eigen-equation can be solved by an algorithm of matrix product states rigorously. The singularity of the entanglement entropy for the one-dimensional quantum analogue provides a stringent criterion to distinguish various phase transitions without identifying any order parameter a prior. Two very close phase transitions are determined at $T_{c1}\approx 0.4459$ and $T_{c2}\approx 0.4532$, respectively. The former corresponding to a Berezinskii-Kosterlitz-Thouless phase transition describing the phase coherence of XY spins, and the latter is an Ising-like continuous phase transition below which a chirality order with spontaneously broken $Z_2$ symmetry is established.

Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions

Recent measurements of charge instabilities in overdoped compounds rekindled the proposal that cuprates become superconductors by long-range order through Josephson coupling between nanoscopic charge domains. We use the theory of phase-ordering dynamics to show that incommensurate charge density waves (CDWs) are formed in the CuO planes by a series of free-energy wells separated by steep barriers. Charge oscillations in these domains give rise to a net hole-hole attraction proportional to the height of these barriers. Concomitantly, the self-consistent calculations yield localized superconducting amplitudes in the CDW domains characterizing a granular superconductor. We show that a transition by long-range phase order promoted by Josephson coupling elucidates many well-known features of cuprates like the high magnetic penetration depth anisotropy and the origin of the pseudogap, among others. Furthermore, the average Josephson energy reproduces closely the planar superfluid density temperature dependence of La-based films and the superconducting giant proximity effects of cuprates, a 20-year-old open problem.

Flat and almost flat bands in the quasi-one-dimensional Josephson junction array

The dispersion law for the linear waves in the quasi-one-dimensional array of inductively coupled Josephson junctions (JJs) is derived. The array has a multiladder structure that consists of the finite number of rows (N ⩾ 2) in Y direction and is infinite in X direction. The spectrum of the linear waves (Josephson plasmons) consists of 2N − 1 branches. Among these branches there is an N-fold completely flat degenerate one that coincides with the Josephson plasma frequency. The remaining N − 1 branches have a standard Josephson plasmon dispersion law typical for 1D JJ arrays. Application of the uniform dc bias on the top of each vertical column of junctions lifts the degeneracy and only one flat branch remains unchanged. The rest of the previously flat branches become weakly dispersive. The parameter range where the flatness of these branches is maximal has been discussed.

Hierarchy of Exact Low-Dimensional Reductions for Populations of Coupled Oscillators.

We consider an ensemble of phase oscillators in the thermodynamic limit, where it is described by a kinetic equation for the phase distribution density. We propose an Ansatz for the circular moments of the distribution (Kuramoto-Daido order parameters) that allows for an exact truncation at an arbitrary number of modes. In the simplest case of one mode, the Ansatz coincides with that of Ott and Antonsen [Chaos 18, 037113 (2008)CHAOEH1054-150010.1063/1.2930766]. Dynamics on the extended manifolds facilitate higher-dimensional behavior such as chaos, which we demonstrate with a simulation of a Josephson junction array. The findings are generalized for oscillators with a Cauchy-Lorentzian distribution of natural frequencies.

Influence of the contact resistance of the YBCO/Au interface on the transport and microwave properties of arrays of high-temperature Josephson junctions

The influence of the contact resistance of the interface of the YBCO/Au structure on the transport and microwave properties of arrays of high-temperature bicrystal Josephson junctions embedded in a coplanar transmission line has been studied. The current-voltage characteristics of Josephson structures fabricated using various technologies are studied: in situ and ex situ with annealing in an oxygen atmosphere. The results obtained can be used to create a quantum ac voltage generator based on high-temperature Josephson junctions. Keywords: high-temperature superconductors, Josephson junctions, microwave, contact resistance.

Влияние контактного сопротивления интерфейса YBCO|Au на транспортные и СВЧ-свойства массивов джозефсоновских контактов из высокотемпературных сверхпроводников

The influence of the contact resistance of the interface of the YBCO/Au structure on the transport and microwave properties of arrays of high-temperature bicrystal Josephson junctions embedded in a coplanar transmission line has been studied. The current-voltage characteristics of Josephson structures fabricated using various technologies are studied: in-situ and ex-situ with annealing in an oxygen atmosphere. The results obtained can be used to create a quantum ac voltage generator based on high-temperature Josephson junctions.

Evaluation of Self-Field Effects in Magnetometers Based on Meander-Shaped Arrays of Josephson Junctions or SQUIDs Connected in Series.

Arrays of superconducting quantum interference devices (SQUIDs) are highly sensitive magnetometers that can operate without a flux-locked loop, as opposed to single SQUID magnetometers. They have no source of ambiguity and benefit from a larger bandwidth. They can be used to measure absolute magnetic fields with a dynamic range scaling as the number of SQUIDs they contain. A very common arrangement for a series array of SQUIDs is with meanders as it uses the substrate area efficiently. As for most layouts with long arrays, this layout breaks the symmetry required for the elimination of adverse self-field effects. We investigate the scaling behavior of series arrays of SQUIDs, taking into account the self-field generated by the bias current flowing along the meander. We propose a design for the partial compensation of this self-field. In addition, we provide a comparison with the case of series arrays of long Josephson junctions, using the Fraunhofer pattern for applications in magnetometry. We find that compensation is required for arrays of the larger size and that, depending on the technology, arrays of long Josephson junctions may have better performance than arrays of SQUIDs.

Current–voltage characteristics of strained, highly underdoped LaSr x CuO4 thin films

The temperature dependence of resistance and of current–voltage characteristics are studied for two underdoped La1.952Sr0.048CuO4 films with different thickness and different degrees of built-in compressive strain. Strain induces an inhomogeneous superconducting (SC) state in the films, with two-step SC transition, consistent with the presence of SC islands coupled by the proximity effect. On further cooling, superfluid density is suppressed and global phase coherence is never reached. Instead, a reentrant increase of resistance appears, reaching several orders of magnitude in the thinner, more strongly strained film, and saturating at lowest temperatures. The saturation is accompanied by Coulomb blockade, which resembles the blockade reported for Josephson junction (JJ) arrays. However, increasing magnetic field quickly diminishes the influence of Coulomb blockade on transport, which is distinct from the behavior observed for JJ arrays. The observation of Coulomb blockade indicates that Cooper pairs survive in the insulating state, suggesting the local character of pairing.

Control of global variables for identical and non-identical Josephson junctions arrays

In the paper a way to solve an LQ-problem for a Josephson junction array with a common LRC-load is proposed. The cases of identical and non-identical Josephson junctions are considered. The solution ensures phase stabilization of Josephson current in every junction. The results are obtained using computer simulation in Jupyter Notebook and MATLAB.

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.

Tunable coupling scheme for implementing two-qubit gates on fluxonium qubits

A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.

On the nonlinear wave transmission in a nonlinear continuous hyperbolic regime with Caputo-type temporal fractional derivative

This present manuscript studies a nonlinear hyperbolic model in fractional form which generalizes the nonlinear Klein–Gordon system. The equation under investigation includes the presence of a time-fractional operator of the Caputo type. A space-fractional form of that equation with integer-order temporal derivative has been previously investigated to elucidate the existence of localized wave transmission in relativistic wave equations. Here, we employ numerical techniques to estimate the solution of the fractional equation. The method has consistency of fourth order in space. Meanwhile, the temporal order of consistency is equal to 3−α. We considered herein a sinusoidal perturbation of the medium. The simulations show the existence of the transmission of localized nonlinear modes in some complex fractional media governed by hyperbolic models. Physically, the present work investigates the phenomenon of nonlinear supratransmission in a continuous generalization of linear chains of harmonic oscillators with memory effects. In particular, the present work corroborates the presence of this nonlinear phenomenon in chains of pendula with memory and arrays of Josephson junctions attached through superconducting wires and memory effects.

Phase interference for probing topological fractional charge in a BiSbTeSe2-based Josephson junction array

Fractional charges can be induced by magnetic fluxes at the interface between a topological insulator (TI) and a type-II superconductor due to axion electrodynamics. In a Josephson junction array with a hole in the middle, these electronic states can have phase interference in an applied magnetic field with period, in addition to the 2π interference of the Cooper pairs. Here, we test an experimental configuration for probing the fractional charge and report the observation of phase interference effect in superconducting arrays with a hole in the middle in both Au- and TI-based devices. Our numerical simulations based on resistive shunted capacitive junction model are in good agreement with the experimental results. However, no clear sign of an axion charge-related interference effect was observed. We will discuss possible reasons and perspectives for future experiments.

Coherent Radiation From Active Josephson Antennas

We performed spectral measurements of two low-temperature discrete Josephson junction (JJ) arrays on a Fourier-transform spectrometer. The arrays contain up to 9000 niobium based junctions located in the area 5 × 5 mm and composed of different designs. The spectrum of each array demonstrates a narrow peak in the frequency range near 140 GHz with the line width 160-170 MHz corresponding to the resolution limit of the spectrometer. It implies the coherent subterahertz radiation from niobium JJ arrays that is necessary for most applications where the JJ array based on similar technology would be implemented. The radiation coherence follows from numerical simulation of Josephson antennas with the self-made algorithm combining the Finite-Difference Time Domain Method with the Resistively and Capacitively Shunted Junction (RCSJ) model. Exploring the spectrum of Beverage-like Josephson antenna simulated by this algorithm we revealed the pure monochromatic emission of all junctions.