Göran Wendin

Andreev bound states in high-Tc superconducting junctions

The formation of bound states at surfaces of materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles with energies inside the superconducting gap Δ may be trapped in bound states in quantum wells, formed by total reflection against the vacuum and total Andreev reflection against the superconductor. Since an electron reflects as a hole and sends a Cooper pair into the superconductor, the surface states give rise to resonant transport of quasiparticle and Cooper pair currents, and may be observed in tunnelling spectra. In superconducting junctions these surface states may hybridize and form bound Andreev states, trapped between the superconducting electrodes. In d-wave superconductors, the order parameter changes sign under 90° rotation and, as a consequence, Andreev reflection may lead to the formation of zero energy quasiparticle bound states, midgap states (MGS). The formation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson current, π-junction behaviour, 0→π junction crossover with temperature, zero-bias conductance peaks, paramagnetic currents, time reversal symmetry breaking, spontaneous interface currents, and resonance features in subgap currents. Taken together these effects, when observed in experiments, provide proof for d-wave superconductivity in the cuprates.

Quantum bits with Josephson junctions

Recent demonstrations of macroscopic quantum coherence in Josephson junction based electronic circuits have opened an entirely new dimension for research and applications in the established field of Josephson electronics. In this article we discuss basic Josephson circuits for qubit applications, methods of quantum description of these circuits, and circuit solutions for qubit couplings. Principles of manipulation and readout of superconducting qubits are reviewed and illustrated with recent experiments using various qubit types.

Nonlinear conductance in molecular devices : Molecular length dependence

We theoretically study the electronic transport in the monolayer of dithiolated phenylene vinylene oligomeres coupled to the (111) surfaces of gold electrodes. We use non-equilibrium Green functions (NEGF) and density functional theory(DFT) implemented in the TranSIESTA package to obtain a full ab initio self-consistent description of the transport current through the molecular nanostructure with different electrochemical bias potentials. The calculated current-voltage characteristics (IVC) of the systems for the same contact geometry have shown a systematic decrease of the conductivity with the increased length of the molecules. We analyze the results in terms of transmission eigenchannels and find that besides the delocalization of molecular orbitals the distance between gold electrodes also determines the transport properties.

Selective coupling of superconducting charge qubits mediated by a tunable stripline cavity

We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux-biased dc superconducting quantum interference device attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is able to accommodate several qubits and allows one to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Critical roles of metal-molecule contacts in electron transport through molecular-wire junctions

We study the variation of electron transmission through Au-S-benzene-S-Au junctions and related systems as a function of the structure of the Au:S contacts. For junctions with semi-infinite flat Au(111) electrodes, the highly coordinated in-hollow and bridge positions are connected with broad transmission peaks around the Fermi level, due to a broad range of transmission angles from transverse motion, resulting in high conductivity and weak dependence on geometrical variations. In contrast, for (unstable) S adsorption on-top of an Au atom, or in the hollow of a 3-Au-atom island, the transmission peaks narrow up due to suppression of large transmission angles. Such more one-dimensional situations may describe more common types of contacts and junctions, resulting in large variations in conductivity and sensitivity to bonding sites, tilting, and gating. In particular, if S is adsorbed in an Au vacancy, sharp spectral features appear near the Fermi level due to essential changes of the level structure and hybridization in the contacts, admitting order-of-magnitude variations of the conductivity. Possibly such a system, can it be fabricated, will show extremely strong nonlinear effects and might work as uni- or bi-directional voltage-controlled two-terminal switches and nonlinear mixing elements. Finally, density-functional theory based transport calculations seem relevant, being capable of describing a wide range of transmission peak structures and conductivities. Prediction and interpretation of experimental results probably require more precise modeling of realistic experimental situations.

Multiple Andreev reflection in single-atom niobium junctions

Single atom junctions between superconducting niobium leads are produced using the Mechanically Controllable Break Junction technique. The current-voltage characteristics of these junctions are analysed using an exact formulation for a superconducting quantum point contact. For tunnelling between two single atoms with a sufficiently large vacuum barrier, it is found that a single channel dominates the current, and that the current-voltage characteristic is described by the theory, without adjustable parameters. For a contact of a single Nb atom it is shown that five conductance channels contribute to the conductance, in agreement with the number expected based on the number of valence orbitals for this d-metal. For each of the channels the transmission probability is obtained from the fits and the limits of accuracy for these numbers are discussed.

Andreev level qubit.

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and readout of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits and discuss the relevant SQUID parameters for qubit operation and readout.

Josephson junction qubit network with current-controlled interaction

We design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighboring qubit loops via local de-current gates. The network allows construction of general N-qubit gates. The proposed design is in line with current main stream experiments.

Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark

We discuss the implementation of an iterative quantum phase estimation algorithm, with a single ancillary qubit. We suggest using this algorithm as a benchmark for multi-qubit implementations. Furthermore we describe in detail the smallest possible realization, using only two qubits, and exemplify with a superconducting circuit. We discuss the robustness of the algorithm in the presence of gate errors, and show that 7 bits of precision is obtainable, even with very limited gate accuracies.