W. Krech

Multiphoton transitions between energy levels in a phase-biased Cooper-pair box

We investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found.

Fabrication of ultrasmall tunnel junctions by electron beam direct-writing

Fabrication of miniaturized tunnel junctions based on high-melting metals by the shadow evaporation technique is rather complicated. The thermal load of the suspended bridge mask during metal evaporation is assumed to be the most serious problem. As an alternative we have developed a preparation technique using e-beam direct-writing lithography in conjunction with material deposition by sputtering. To test the preparation process, we have fabricated single electron transistors (SETs) based on the metals Al and Nb, including mixed Al/Nb samples. For SETs made completely of Nb, we preferred Al0/sub x/ to the natural oxide NbO/sub x/ for barrier generation. The yield of functioning samples amounted to about 80%. By means of simple considerations we have estimated the tunnel capacitances to be of the order of a few 10/sup -16/ F, the tunnel resistance spread was less than one order of magnitude.

Linear microwave response of a superconducting charge qubit

We present results of an analytical study of a superconducting charge qubits linear response to a microwave field. Coherence of the states of the autonomous device arises from the competition of irradiation and dephasing that is formulated by means of a relaxation rate. Due to this quantum effect the qubit impedance is expressed in terms of quantum resistance unit, quality, and detuning. The theoretical results could help to design microwave experiments for determining the qubits dephasing time. q 2000 Elsevier Science B.V. All rights reserved.

THEORY OF PHASE LOCKING IN SMALL JOSEPHSON-JUNCTION CELLS

Within the RSJ model, we performed a theoretical analysis of phase-locking in elementary strongly coupled Josephson junction cells. For this purpose, we developed a systematic method allowing the investigation of phase-locking in cells with small but non-vanishing loop inductance. The voltages across the junctions are found to be locked with very small phase difference for almost all values of external flux. However, the general behavior of phase-locking is found to be just contrary to that according to weak coupling. In case of strong coupling there is nearly no influence of external magnetic flux on the phases, but the locking-frequency becomes flux-dependent. The influence of parameter splitting is considered as well as the effect of small capacitive shunting of the junctions. Strongly coupled cells show synchronization even for large parameter splitting. Finally, a study of the behavior under external microwave radiation shows that the frequency locking-range becomes strongly

Preparation of self‐aligned in‐line tunnel junctions for applications in single‐charge electronics

The self‐aligned in‐line technique has been applied to the preparation of ultrasmall low‐capacitance metallic tunnel junctions. By using e‐beam lithography the area of Al/AlOx/Al contacts has so far been reduced to less than 0.005 μm2. At low temperatures high‐ohmic double junctions with a small metallic island between them show the Coulomb blockade effect. The current through such a device could be modulated by a voltage applied to a gate electrode capacitively coupled to the island (single‐electron transistor). Both single‐charge phenomena have been observed at temperatures up to 1 K.

Electronic cooling in superconducting tunnel junctions

Abstract The cooling power provided by the current through a superconductor/insulator/superconductor tunnel junction is studied theoretically. The influence of non-equilibrium distributions of the quasi-particles on the heat flow is analysed within a simple relaxation model. A superconducting gap enhancement can be explained within the equilibrium as well as the non-equilibrium model.

Single-electron transistors based on Al/AlO/sub x//Al and Nb/AlO/sub x//Nb tunnel junctions

As an alternative to the shadow evaporation method for the preparation of ultrasmall tunnel junctions we have established the so-called self-aligned in-line technique. It was applied to the fabrication of common Al/AlO/sub x//Al-type and, for the first time, Nb/AlO/sub x//Nb-based single-electron transistors. The characterization of the samples at temperatures in the range of a few hundred millikelvins reveals charging effects (Coulomb blockade and gate modulation) of the quasiparticle current.

Fabrication and measurement of metallic single electron transistors

Using the so-called self-aligned in-line technique, we have fabricated single electron transistors based on the metals aluminum, tantalum and chromium. The material deposition was carried out without exception by sputtering. The samples were electrically characterized both in a dilution refrigerator and in a helium-3 cryostat. In case of transistors made completely of (superconducting) aluminum we observed in the modulation characteristics deviations from the predictions of the orthodox theory of sequential quasiparticle tunneling. They are caused by additional current contributions due to Josephson-quasiparticle cycles. Furthermore, we report on the low-temperature behavior of mixed single electron transistors made of tantalum and chromium islands, respectively, between aluminum oxide barriers and external aluminum electrodes.

ELECTROMETRIC SENSITIVITY OF THE SINGLE ELECTRON TRANSISTOR

The essential part of the SET electrometer is the so-called SET transistor which consists of two serially coupled SET junctions driven by an external voltage. An external charge is influenced on the island between the two junctions. Furthermore, the influence of the electromagnetic environment is modelled by an additional impedance in the circuit. Using as well the two-state as the three-state approach, the mean-current through the double-junction, the shot-noise parameters and the charge sensitivity are calculated as a function of the driving voltage and the external charge on the island.

Antiphase locking in a two‐dimensional Josephson junction array

We consider theoretically phase locking in a simple two‐dimensional Josephson junction array consisting of two loops coupled via a joint line transverse to the bias current. Ring inductances are supposed to be small, and special emphasis is taken on the influence of external flux. It is shown that in the stable oscillation regime both cells oscillate with a phase shift equal to π (i.e., antiphase). This result may explain the low radiation output obtained so far in two‐dimensional Josephson junction arrays experimentally.