Fast Algorithms For Josephson Junction Arrays : Bus--bars and Defects

We report measurements of the dependence on magnetic field and array size of the resistive transition of Josephson junction arrays with long-range interaction. Because every wire in these arrays has a large number of nearest-neighbors (9 or 18 in our case), a mean-field theory should provide an excellent description of this system. Our data agree well with this mean-field calculation, which predicts that Tc (the temperature below which the array exhibits macroscopic phase coh...

Josephson junction arrays can be used as quantum channels to transfer quantum information between distant sites. In this work we discuss simple protocols to realize state transfer with high fidelity. The channels do not require complicate gating but use the natural dynamics of a properly designed array. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges, as well as the effect of dynamical noise. We...

We study experimentally and numerically the zero-voltage supercurrent vs. magnetic field of non-uniform arrays of Josephson junctions parallel-connected by a superconducting stripline. The measured curves are complex, unique and in excellent agreement with numerical simulations using a specially developed model. Using this, we can optimize the arrays to have any desired interference pattern. Such new devices could find applications in magnetometry, quasiparticle mixers and de...

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 cruciall...

Measurements performed on superconductive networks shaped in the form of planar graphs display anomalously large currents when specific branches are biased. The temperature dependencies of these currents evidence that their origin is due to Cooper pair hopping through the Josephson junctions connecting the superconductive islands of the array. The experimental data are discussed in terms of a theoretical model which predicts, for the system under consideration, an inhomogeneo...

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunnelling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalisation of the Hamiltonian operator is used in order to reliably parametrise the effects due to inhom...

The dynamics of thermally excited vortices in a dilute two-dimensional Josephson junction array where a fraction of the superconducting islands is missing has been investigated using a multiple trapping model. An expression for the frequency dependent mobility of vortices has been calculated which allows to obtain the frequency dependent complex electrodynamic response of the array for different fractions of missing islands.

We show analytically that the inverse kinetic inductance $L^{-1}$ of an overdamped junction array at low frequencies is proportional to the admittance of an inhomogeneous equivalent impedance network. The $ij^{th}$ bond in this equivalent network has an inverse inductance $J_{ij}\cos(\theta_i^0-\theta_j^0-A_{ij})$, where $J_{ij}$ is the Josephson coupling energy of the $ij^{th}$ bond, $\theta_i^0$ is the ground-state phase of the grain $i$, and $A_{ij}$ is the usual magnetic ...

The standard theory of dynamical Coulomb blockade [$P(E)$ theory] in ultra-small tunnel junctions has been formulated on the basis of phase-phase correlations by several authors. It was recently extended by several experimental and theoretical works to account for novel features such as electromagnetic environment-based renormalization effects. Despite this progress, aspects of the theory remain elusive especially in the case of linear arrays. Here, we apply path integral for...

Dislocations and disclinations in a lattice of Josephson junctions will affect the dynamics of vortex excitations within the array. These defects effectively distort the space in which the excitations move and interact. The interaction energy between such defects and excitations are determined and vortex trajectories in twisted lattices are calculated. Finally, possible experiments observing these effects are presented.