Two-dimensional arrays of very-small-capacitance Josephson junctions have been studied. At low temperatures the arrays show a transition from superconducting to insulating behavior when the ratio of charging energy to Josephson-coupling energy exceeds the value 1. Insulating behavior coincides with the occurrence of a charging gap inside the BCS gap, with an S-shaped I-V characteristic. This so far unobserved S shape is predicted to arise from macroscopic quantum coherent effects including Bloch oscillations.

We study experimentally the low temperature resistance of superconducting nanowires connected to normal metal reservoirs. We find that a substantial fraction of the nanowires is resistive, down to the lowest temperature measured, indicative of an intrinsic boundary resistance due to the Andreevconversion of normal current to supercurrent. The results are successfully analyzed in terms of the kinetic equations for diffusive superconductors.

The electrical properties of microfabricated nanobridges of copper, silver, and gold with contact diameters in the range 4 -32 nm have been studied. High-quality point-contact spectra are evidence that electron transport is ballistic in these nanobridges. A comparison of our spectra with spectra from mechanical point contacts shows that microfabricated nanobridges are at least as good as mechanical point contacts for study of the electron-phonon interaction. Further, in Au nanobridges we have observed defect motion induced two-level resistance fluctuations (TLFs). An expression is derived for the voltage dependence of the temperature Tz of a defect in a nanobridge at low lattice temperatures. Using this expression for Tz, the experimental voltage dependence of the TLF's is successfully described by a thermal-activation model for the fluctuation rates, in which the voltage dependence of the activation energy and defect temperature is included. The values for the attempt time, activation energy, and electromigration parameter are as expected for defects in metals. An analysis of the two TLF's studied, showing a striking difference in both voltage dependence and magnitude of the duty cycle, suggests that rearrangement of complex defects is the mechanism behind the TLF behavior.

The authors have studied low-frequency resistance fluctuations in shadow-evaporated Al/ AlO x /Al tunnel junctions. Between 300 and 5 K the spectral density follows a 1 / f law. Below 5 K, individual defects distort the 1 / f shape of the spectrum. The spectral density decreases linearly with temperature between 150 and 1 K and saturates below 0.8 K. At 4.2 K, it is about two orders of magnitude lower than expected from a recent survey ͓D. J. Van 4 Decoherence due to external sources such as the measurement devices has been studied extensively and is by now well understood, 5 permitting qubit dephasing times of up to several microseconds. 6 Future progress in this field of research depends crucially on understanding and controlling decoherence due to defects in the devices. 7-9 Superconducting qubits contain Josephson junctions, whose Josephson energy, E J = ⌽ 0 I C / ͑2 ͒, determines the potential landscape of the qubit ͑I C is the critical current and ⌽ 0 = h /2e is the superconducting flux quantum͒. Due to imperfections of the tunnel barrier, E J fluctuates in time, leading to fluctuations in the qubit potential. Therefore, the qubit energy splitting is not constant during an experiment, which leads to decoherence.

Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip (QPS) processes replacing the tunneling of Cooper pairs. When the QPS amplitude E S is much smaller than the inductive energy E L , the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of E S /E L is discussed and compared with earlier experimental results. For one-dimensional and twodimensional arrays of nanowires quantum phase transitions are expected as a function of E S /E L . They can be tuned by a homogeneous magnetic frustration.