Richard L. Kautz

Picosecond pulses on superconducting striplines

The attenuation and phase velocity of a superconducting thin‐film stripline are calculated at high frequencies using the theory of Mattis and Bardeen. These results are used to study the propagation of picosecond pulses which have frequency components approaching the superconducting energy‐gap frequency.

Josephson D/A converter with fundamental accuracy

A binary sequence of series arrays of shunted Josephson junctions is used to make a 14-b D/A converter. With 13 bias lines, any step number in the range -8192 to +8192 -1.2 V to +1.2 V can be selected in the time required to stabilize the bias current (a few microseconds). The circuit is a fast accurate dc reference, and it makes possible the digital synthesis of ac waveforms whose amplitudes derive directly from the internationally accepted definition of the volt. >

Noise in the Coulomb blockade electrometer

We have measured the noise of a Coulomb blockade electrometer. Below 100 Hz, the noise referred to the input charge has a 1/f power spectrum with a charge noise of 3×10−4 e/√Hz and an energy sensitivity EN of 3×104 ℏ at 10 Hz. The 1/f noise probably results from the stochastic occupation of charge traps which could in principle be eliminated. The theoretical noise floor is set by shot noise, and indirect measurements show that this contribution to EN can be as small as 1.5 ℏ, suggesting that the electrometer will be a quantum limited amplifier if the 1/f noise can be eliminated.

Survey of chaos in the rf‐biased Josephson junction

Chaotic behavior in the rf‐biased Josephson junction is studied through digital simulations of the Steward–McCumber model. Chaotic states are characterized by Poincare sections, Liapunov exponents, and power spectra. Models are presented which explain some features of the chaotic spectra. The parameter range over which chaotic behavior occurs is determined empirically for a broad range of dc bias, rf bias, and hysteresis parameters for a fixed rf frequency. It is shown that chaos does not occur if either the dc bias or the rf bias is very large. An attempt is made to explain the boundaries of the chaotic region in terms of simple models for chaotic behavior.

The ac Josephson effect in hysteretic junctions: Range and stability of phase lock

The rf‐induced constant voltage steps generated by the ac Josephson effect are studied within the context of the Stewart‐McCumber model. Simulations are used to determine the range of current bias over which phase lock occurs for model parameters appropriate to hysteretic tunnel junctions. The effect of noise on phase lock is also considered. The results are applied to a zero‐bias voltage standard proposed by Levinsen et al.

Microwave‐induced constant‐voltage steps at one volt from a series array of Josephson junctions

It is demonstrated that a series array of 1474 Josephson junctions can produce quantized voltages up to 1.2 V when driven by microwaves at 90 GHz in the absence of a dc bias. This result brings closer the possibility of a practical Josephson voltage standard at the 1‐V level.

Series-array Josephson voltage standards

Series arrays typically including 1500 Josephson junctions driven at 90 GHz have been used to generate quantized reference voltages in excess of 1 V. Such standards simplify the procedure and reduce the measurement uncertainities in the calibration of electrochemical cells.

Chaotic states of rf‐biased Josephson junctions

The existence of chaotic solutions to the rf‐driven Stewart‐McCumber model of a Josephson junction has recently been demonstrated. The present paper describes more fully the range of junction parameters and frequencies for which chaotic solutions occur, details the connection between chaotic states and instabilities in phase‐lock, and shows that chaotic noise can be much larger than the thermal noise of a junction.

Noise, chaos, and the Josephson voltage standard

The design of zero-bias Josephson voltage standards is presented as a case study in nonlinear dynamics. Based on superconducting tunnel junctions, such standards rely on nonlinearity to create a phase lock between an internal junction variable and an applied rf bias. In the terminology of nonlinear dynamics, phase lock corresponds to motion on a periodic attractor. Not all attractors of the rf-biased junction are periodic, however, and both quasiperiodic and chaotic attractors must be avoided in voltage standards. Surprisingly, the optimum operating point for zero-bias standards is near a region of chaos. Thus, the Josephson coupling energy , a measure of the junctions nonlinearity, must be chosen much larger than the thermal energy to avoid disruption by intrinsic noise but not so large that chaos is evoked. The optimum maximizes the activation energy required for thermally induced escape from the phase-locked attractor. For nonequilibrium systems like the rf-biased junction, is a difference in quasipotential that can be calculated by finding the most probable path for escape from a basin of attraction in the limit of low temperature.

Self‐heating in the Coulomb‐blockade electrometer

A detailed comparison between theory and experiment is used to demonstrate the presence of self‐heating in the Coulomb‐blockade electrometer. When three different heating models are considered, the best fit with experimental electrometer characteristics is obtained for a model in which the electron temperature of the island electrode is determined by heat transfer to the lattice via electron‐phonon coupling. In the successful model, the temperature Ti of the island electrons is related to the power Pi dissipated in the island and the temperature Tl of the phonons by Pi=ΣΩ(Ti5−Tl5), where Σ is an electron‐phonon coupling parameter characteristic of the island material and Ω is the volume of the island. The best fit between theory and experiment yields a value of Σ=0.2 nW/K5/μm3 for the electron‐phonon coupling in aluminum. Our calculations show that the electron temperature of the island commonly exceeds 100 mK even when the lattice remains at 35 mK.