We report on the realization of a superinductor, a dissipationless element whose microwave impedance greatly exceeds the resistance quantum RQ. The design of the superinductor, implemented as a ladder of nanoscale Josephson junctions, enables tuning of the inductance and its nonlinearity by a weak magnetic field. The Rabi decay time of the superinductor-based qubit exceeds 1 µs. The high kinetic inductance and strong nonlinearity offer new types of functionality, including the development of qubits protected from both flux and charge noises, fault tolerant quantum computing, and high-impedance isolation for electrical current standards based on Bloch oscillations. PACS numbers: 74.50.+r, 74.81.Fa, 85.25.Am Superinductors are desired for the implementation of the electrical current standards based on Bloch oscillations [1,2], protection of Josephson qubits from the charge noise [3,4], and fault tolerant quantum computation [5,6]. The realization of superinductors poses a challenge. Indeed, the "geometrical" inductance of a wire loop is accompanied by a sizable parasitic capacitance, and the loop impedance Z does not exceed αR Q [7], where α = 1/137 is the fine structure constant and2 is the resistance quantum. This limitation does not apply to superconducting circuits whose kinetic inductance L K is associated with the inertia of the Cooper pair condensate [8].The kinetic inductance of a Josephson junction,2 /E J , scales inversely with its Josephson energy E J [8] (Φ 0 = h/2e is the flux quantum). The kinetic inductance can be increased by reducing the inplane junction dimensions and, thus, E J . However, this resource is limited: with shrinking the junction size, the charging energy E C = e 2 /2C (C is the junction capacitance) increases and the phase-slip rategrows exponentially, which leads to decoherence. Small Josephson energy (i.e., large kinetic inductance) can be realized in chains of dc SQUIDs frustrated by the magnetic field [9,10]. However, the phase-slip rate increases greatly with frustration, and the chains do not provide good isolation from the environment. For the linear chains of Josephson junctions with E J /E C ≫ 1, relatively large values of L K (up to 300 nH [3]) have been realized in the phase-slip-free regime; further increase of the impedance of these chains is hindered by the growth of their parasitic capacitance. Also, the linear chains, as well as the nanoscale superconducting wires with a kinetic inductance of ∼ 10 nH/µm [11,12], are essentially linear elements whose inductance is not readily tunable (unless large currents are applied).We propose a novel superinductor design that has several interesting features. This circuit can be continuously tuned by a weak magnetic field between the regimes characterized by a low linear inductance and a very large nonlinear inductance. Importantly, the large impedance Z ≫ R Q is realized when the decoherence processes associated with phase slips are fully suppressed. This combination of strong nonlinearity and low decoherence rate is an asset ...

Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense configuration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task.

We consider the scattering matrix approach to quantum electron transport in meso-and nanoconductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and is often more efficient for coherent conductors (especially when proving general relations) and typically more transparent. We provide a description of both time-averaged quantities (for example, current±voltage characteristics) and current fluctuations in time Ð noise, as well as full counting statistics of

A new critical-current-by-design paradigm is presented. It aims at predicting the optimal defect landscape in superconductors for targeted applications by elucidating the vortex dynamics responsible for the bulk critical current. To this end, critical current measurements on commercial high-temperature superconductors are combined with large-scale time-dependent Ginzburg-Landau simulations of vortex dynamics.

Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusions using large-scale numerical simulations of time-dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corresponds to 15-23% of the total volume being replaced by nonsuperconducting material. For fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that the optimal particle diameter slowly decreases with the magnetic field from 4.5 to 2.5 coherence lengths at a given temperature. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.