We have measured the current-phase relationship I(ϕ) of symmetric 45 • YBa2Cu3O7−x grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature T , a local minimum at a temperature T * . (ii) At T ≈ T * , the first harmonic of I(ϕ) changes sign. (iii) For T < T * , the second harmonic of I(ϕ) is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between d-wave superconductors.The most important phenomenological difference between the high-T c cuprates and conventional superconductors regards the orbital symmetry of the superconducting order parameter. In the cuprates the pair potential changes sign depending on the direction in momentum space according to 1,2 ∆(ϑ) = ∆ 0 cos 2(ϑ − θ), where ϑ is the angle between the wave vector and the (laboratory) x-axis, while θ is the angle between the Cu-Cu bond direction of the superconductor and the x-axis. This unconventional d-wave symmetry was predicted 3 and experimentally confirmed 1,2 to be directly measurable in the Josephson effect between a high-T c and a conventional superconductor. Another consequence of the dwave symmetry is that mid-gap states (MGS) with energy ε = 0 should form on the free surface of a d-wave superconductor if ∆(ϑ) has opposite signs on incident and reflected electronic trajectories. 4 The MGS density must be maximal for (110)-like surfaces and this prediction has in fact been confirmed by STM microscopy on YBCO single crystals 5 which revealed the MGS contribution to the YBCO tunneling density of states. The presence of the MGS is expected to influence in a spectacular way also the Josephson effect in junctions between d-wave superconductors with different crystallographic orientations. Yet no clear manifestation of the MGS in the Josephson effect in such junctions has been observed so far, which is a challenge for the concept of d-wave superconductivity in the cuprates.Moreover, due to possible applications in quantum computing, 6,7 there is substantial interest in Josephson junctions and circuits with a doubly degenerate ground state. Such a state was predicted in an asymmetric 45 • junction (θ 1 = 0 • and θ 2 = 45 • , the angles θ 1,2 are defined in Fig. 1), since odd harmonics of the Josephson current I(ϕ) = n I n sin nϕ are suppressed by symmetry. 8,9The current-phase relation observed in Ref. 10 indeed showed a substantial contribution of the second harmonic I 2 . However, there is a finite supercurrent flowing along the interface in the ground state of asymmetric 45 • junctions. 9 Therefore they do not lead to completely quiet qubits in the sense of Ref. 6. Motivated by the search for both, the MGS in high-T c Josephson junctions and a quiet qubit, we have studied symmetric 45 • junctions (i.e. junctions with θ 1 = −θ 2 = 22.5 • ). In this paper we report the fir...

We present an experimental and theoretical study of the current-phase relation I s () for 45°grain boundaries in YBa 2 Cu 3 O 7Ϫx films. A model of strongly inhomogeneous Josephson junctions, in which the presence of randomly alternating current leads to a deviation of I s () from the well-known sin() dependence, has been used. This deviation decreases with the temperature T and is described by the formula I s ()ϭI c (T)(sin ϩ␥(T)sin2). Using the developed model, the coefficient ␥ is calculated and its temperature dependence is found to be in good agreement with experiment.

Single layer autonomous high-Tc dc superconducting quantum interference devices (SQUIDs) have been fabricated and tested. The SQUIDs were designed for application as a galvanometer. The current to be measured is injected directly in a microstrip segment of the SQUID loop. Step-edge as well as bicrystal YBCO Josephson junctions were used. We consider two aspects: (i) optimization of the noise properties with respect to current resolution, and (ii) temperature dependence of the period of voltage-flux relation. The SQUID inductance was calculated numerically taking into account the magnetic field penetration depth λ. The temperature dependence of λ(T) was obtained from experimental results and is found to be in good agreement with λ(T)≊λ(0)[1−(T/TC)2]−1/2.

We implement a classical counterpart of a scalable design for adiabatic quantum computation.The key element of this design is a coupler providing controllable coupling between two bistable elements (in our case superconducting rings with a single Josephson junction playing the role of a classical counterpart of superconducting flux qubits). The coupler is also a superconducting ring with a single Josephson junction that operates in the nonhysteretic mode with a screening parameter of about 0.9. The flux-coupling between two bistable rings can be controlled by changing the magnetic flux through the coupler. Since the coupling amplitude is proportional to the derivative of the coupler's current-flux relation, the coupling can be tuned from ferromagnetic to anti-ferromagnetic. In between the coupling can also be switched off. PACS numbers: 85.25.DqThe magnetic properties of a single-junction interferometer (superconducting loop with one Josephson junction) depend on its normalized critical current β = 2πLI C /Φ 0 only. Here L is the loop inductance, I C the critical current of the junction and Φ 0 is the flux quantum. If β > 1 such an interferometer exhibits a double degenerated energy state if an external flux equal to half a flux quantum is applied (degeneracy point) 1 . Close to the degeneracy point, the single junction ring is a bistable element with two magnetic moments corresponding to the superconducting screening currents flowing clockwise and counterclockwise. These two states can be described in spin formalism by making use of Pauli matrices. In other words, a system of magnetically coupled interferometers is a realization of a two-dimensional Ising spin system. When the coupling between spins is randomly distributed the system represents a spin glass. The problem of finding the ground state of such a system is a nonpolynomial one, i.e., the amount of calculation resources needed grows exponentially with the number of elements. Mathematically this task is equivalent to solving the socalled MAXCUT problem. 2 Recently, the implementation of an adiabatic quantum algorithm 3 by making use of superconducting flux qubits has been proposed. 4,5 Schematically, the implementation is the same as for the 2D Ising model described above but instead of classical bits quantum bits (qubits) are used. It has been shown that such a quantum system could solve the problem discussed above in polynomial time. In this letter we present the realization of a scalable classical design implementing the 2D Ising model with a coupling which can be tuned from antiferromagnetic, through zero, to ferromagnetic.Theoretically several schemes of tunable coupling were proposed 6,7 and also some implemented. 8,9 In the design presented here we use the approach proposed by Maassen van den Brink et al. 10 Here a coupler, realized as a single-junction interferometer with β CO = 2πL CO I C /Φ 0 < 1, provides tunable coupling between two bistable elements. The coupling amplitude J can be varied by changing the magnetic flux through the coupler. Th...