Phase-Charge Duality of a Josephson junction in a fluctuating electromagnetic environment

We have measured the current-voltage characteristics of a single Josephson junction placed in a high impedance environment. The transfer of Cooper pairs through the junction is governed by overdamped quasicharge dynamics, leading to Coulomb blockade and Bloch oscillations. Exact duality exists to the standard overdamped phase dynamics of a Josephson junction, resulting in a dual shape of the current-voltage characteristic, with current and voltage changing roles. We demonstrate this duality with experiments which allow for a quantitative comparison with a theory that includes the effect of fluctuations due to finite temperature of the electromagnetic environment

Single-electron current sources: towards a refined definition of ampere

Controlling electrons at the level of elementary charge $e$ has been demonstrated experimentally already in the 1980's. Ever since, producing an electrical current $ef$, or its integer multiple, at a drive frequency $f$ has been in a focus of research for metrological purposes. In this review we first discuss the generic physical phenomena and technical constraints that influence charge transport. We then present the broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently "just" wild ideas, still often potentially competitive if technical constraints can be lifted. We also discuss the important issues of read-out of single-electron events and potential error correction schemes based on them. Finally, we give an account of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and briefly discuss the applications and uses of single-electron devices outside the metrological context.Comment: 55 pages, 38 figures; (v2) fixed typos and misformatted references, reworded the section on AC pump

Array of Josephson junctions with a non-sinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act respectively by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO$_2$ planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to $p=1/8$, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions.Comment: Added: comparison with experiments; reference

Cooper pair transport in arrays of Josephson junctions = Cooperpaartransport in Feldern von Josephson-Kontakten

In this work, the fabrication, measurement and analysis of several one-dimensional SQUID arrays is described. The temperature and flux dependence of the thermally activated charge transport is analysed, and compared to a theoretical model

Correlated transport through junction arrays in the small Josephson energy limit: incoherent Cooper-pairs and hot electrons

We study correlated transport in a Josephson junction array for small Josephson energies. In this regime transport is dominated by Cooper-pair hopping, although we observe that quasiparticles can not be neglected. We assume that the energy dissipated by a Cooper-pair is absorbed by the intrinsic impedance of the array. This allows us to formulate explicit Cooper-pair hopping rates without adding any parameters to the system. We show that the current is correlated and crucially, these correlations rely fundamentally on the interplay between the Cooper-pairs and equilibrium quasiparticles.Comment: 11 pages, 9 figures - Published Versio

Current measurement by real-time counting of single electrons

The fact that electrical current is carried by individual charges has been known for over 100 years, yet this discreteness has not been directly observed so far. Almost all current measurements involve measuring the voltage drop across a resistor, using Ohm's law, in which the discrete nature of charge does not come into play. However, by sending a direct current through a microelectronic circuit with a chain of islands connected by small tunnel junctions, the individual electrons can be observed one by one. The quantum mechanical tunnelling of single charges in this one-dimensional array is time correlated, and consequently the detected signal has the average frequency f=I/e, where I is the current and e is the electron charge. Here we report a direct observation of these time-correlated single-electron tunnelling oscillations, and show electron counting in the range 5 fA-1 pA. This represents a fundamentally new way to measure extremely small currents, without offset or drift. Moreover, our current measurement, which is based on electron counting, is self-calibrated, as the measured frequency is related to the current only by a natural constant.Comment: 9 pages, 4 figures; v2: minor revisions, 2 refs added, words added to title, typos correcte

Charge-4e supercurrent in an InAs-Al superconductor-semiconductor heterostructure

Superconducting qubits with intrinsic noise protection offer a promising approach to improve the coherence of quantum information. Crucial to such protected qubits is the encoding of the logical quantum states into wavefunctions with disjoint support. Such encoding can be achieved by a Josephson element with an unusual charge-4e supercurrent emerging from the coherent transfer of pairs of Cooper-pairs. In this work, we demonstrate the controlled conversion of a conventional charge-2e dominated to a charge-4e dominated supercurrent in a superconducting quantum interference device (SQUID) consisting of gate-tunable planar Josephson junctions (JJs). We investigate the ac Josephson effect of the SQUID and measure a dominant photon emission at twice the fundamental Josephson frequency together with a doubling of the number of Shapiro steps, both consistent with the appearance of charge-4e supercurrent. Our results present a step towards novel protected superconducting qubits based on superconductor-semiconductor hybrid materials