Purpose Josephson junctions act as active elements in superconducting electronics. The behavior of this nonlinear element is characterized by the relation between current and the quantum mechanical phase‐difference. For an accurate device modeling, detailed knowledge about this relation is necessary. This paper aims to discuss these issues. Design/methodology/approach To obtain detailed information, a method for DC measurement of the current‐phase relation suitable for all kinds of superconducting circuit elements was accomplished. Findings The authors developed a linear transformation algorithm to calculate the current‐phase relation from the measured data. Research limitations/implications It turns out that in future designs additional connections and special test structures are required to gain more knowledge about inductance values required for the algorithm. Originality/value Based on the inverse calculation of that algorithm, the authors found a 7 percent deviation of the current‐phase relation of a standard superconductor/insulator/superconductor Josephson junction from the predicted sine‐wave behavior. Furthermore, the paper suggests to use this method to evaluate the current‐phase relation of new Josephson elements such as a superconductor/ferromagnet/superconductor junction. Therefore, the authors will deposit the new element directly on the chip with the test setup fabricated with standard Nb‐technology.
This review provides a theoretical basis for understanding the current-phase relation (C\ensuremath{\Phi}R) for the stationary (dc) Josephson effect in various types of superconducting junctions. The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the C\ensuremath{\Phi}R from the standard sinusoidal form. A new experimental tool for measuring the C\ensuremath{\Phi}R is described and its practical applications are discussed. The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy. A number of examples illustrate the importance of the C\ensuremath{\Phi}R measurements for both fundamental physics and applications.
We study the current-phase relations of superconductor-constriction-superconductor Josephson junctions made from platinum silicide thin films by fabricating dc-superconducting quantum interference devices incorporating pairs of junctions and measuring their magnetic-field-dependent electrical transport. By comparing the supercurrent interference patterns with numerical Ginzburg-Landau simulations, we extract the current-phase relations of individual junctions and quantify the degree of nonlinearity. These measurements show that while the constrictions themselves sustain substantial nonlinearity, the effect is moderated by the kinetic inductance of the device leads, which is an important consideration for practical superconducting circuit applications.
Josephson junctions are the central nonlinear element of superconducting qubits, yet their standard description is reached through a chain of approximations. We propose a purely quantum-mechanical model of the junction, formulated directly in Hilbert space: a charged particle moves on a one-dimensional loop, and the junction is a point at which the wave function obeys self-adjoint boundary conditions, labelled by a coupling strength
λ, which controls the transparency of the junction, and a phase jump
δ, which plays the role of the superconducting phase difference. For a loop with a single junction we solve the spectral problem and show that the ground-state momentum expectation, identified with the supercurrent, factorises exactly as
⟨p^0⟩=Ic(δ,λ)sinδ. For opaque junctions
Ic becomes independent of
δ and the first Josephson relation
I=Icsinδ is recovered; for strongly attractive coupling, where the ground state is bound to the junction, the
sinδ law is also recovered, but with an exponentially suppressed amplitude. For more transparent junctions, however, the model \emph{predicts} deviations from the pure
sinδ law:
Ic acquires a dependence on
δ already at order
λ−2, compatible with the higher Josephson harmonics recently found necessary to describe superconducting qubit spectra, and a fully transparent contact yields a current linear in
δ. When the phase varies in time, a gauge transformation shows that the voltage drop across the junction is proportional to
δ˙, so that the second Josephson relation emerges without being imposed. The boundary-condition approach thus reproduces both Josephson relations from first principles and predicts corrections to them, offering a route towards higher-fidelity models of superconducting qubits.
Conventional superconductor/insulator/superconductor (SIS) Josephson junctions, devices where two superconductors are separated by a tunnel barrier are technologically important as elements in quantum circuits, particularly with their key role in superconducting qubits. An important characteristic of Josephson junctions is the relation between the supercurrent Is and the phase difference
ϕ between them. For SIS junctions, the current-phase relation is sinusioidal and 2
π periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have non-sinusoidal current-phase relations that are still 2
π periodic. We show here that a multi-terminal diffusive SNS Josephson junction with 4 superconducting contacts can show a current phase relation between two of the contacts that is a superposition of 2
π and 4
π periodic components whose relative strength is controlled by the phase difference between the other two contacts, becoming 2
π or 4
π periodic for certain values of this phase difference. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.
The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit.