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IEEE Transactions on Magnetics

Sensitivity of the balanced Josephson-junction comparator

Timur V. Filippov, Victor K. Kornev

Published Mar 1, 1991• 40 citations
Publisher

Abstract

The sensitivity of a balanced comparator composed of two overdamped Josephson junctions fed by single flux pulses is calculated, taking into account both thermal and quantum fluctuations. The results of the analysis are compared with those of recent experiments. Ultimate resolution of the balanced comparator with feasible junction parameters is estimated to be as high as approximately 50 pA/Hz/sup 1/2/ at 4 K and approximately 10 pA/Hz/sup 1/2/ at T to 0 K. Performance limits of the device are compared with those of its single-junction counterpart.

DOI
10.1109/20.133715

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The sensitivity of a balanced comparator composed of two overdamped Josephson junctions fed by single flux pulses is calculated, taking into account both thermal and quantum fluctuations. The results of the analysis are compared with those of recent experiments. Ultimate resolution of the balanced comparator with feasible junction parameters is estimated to be as high as approximately 50 pA/Hz/sup 1/2/ at 4 K and approximately 10 pA/Hz/sup 1/2/ at T to 0 K. Performance limits of the device are compared with those of its single-junction counterpart.
We have extended our previous study of SFQ balanced comparators which use two overdamped Josephson junctions to (a) finite sampling rate and (b) junctions with higher critical current density. The effective width /spl Delta/I/sub x/ of the gray zone of the comparators fabricated using the niobium-trilayer technology of HYPRES, Inc. (j/sub c//spl ap/1 kA/cm/sup 2/) and Stony Brook's domestic planarized process (j/sub c//spl ap/5 kA/cm/sup 2/) has been measured as a function of the SFQ pulse rate (from 2.5 to 55 GHz) and temperature (from 1.6 to 4.2 K), for various drivers which determine the SFQ pulse shape and external impedance. The data have been compared with available theories of Josephson junction dynamics in the presence of thermal and quantum fluctuations. We have found that /spl Delta/I/sub x/ can be substantially reduced by using relatively broad ("soft") SFQ pulses. For high-j/sub c/ comparators fed by short (/spl sim/2-ps) SFQ pulses the temperature dependence is practically negligible, indicating the dominance of quantum fluctuations.
The use of high-T/sub c/ Josephson junctions for digital applications requires a careful study of the influence of thermal noise on circuit performance. We investigated a balanced current comparator, which contains a basic component of all RSFQ circuits: two overdamped Josephson junctions connected in series. The dependence of the dc-voltage across the Josephson junctions on signal current was measured to determine the threshold uncertainty of switching of the comparator. The experimental data obtained at different sampling pulse frequencies, in a temperature range from 10 to 50 K, were compared with a theoretical model, taking into account the influence of thermal noise as well as of sampling pulse frequency.
The process of reproduction of single flux quantum pulses in a Josephson junction chain composed of a pulse generator, a balanced comparator, and a single Josephson junction is investigated. It is shown that the reproduction of single flux quantum pulses in such a chain is more stable and the mean and the standard deviation of switching time are minimal for the McCumber-Stewart parameter value from 0.5 to 1 and for a normalized clock generator current around 1.5. The influence of input and output inductances on the characteristics of a balanced comparator is investigated. The recommended value of the output inductance leading to smooth pulses and relatively small jitter is around unity.
We consider the time characteristics of a balanced comparator formed by two Josephson junctions connected in series. Such a decision-making junction pair is an essential component of all RSFQ cells. The analysis is performed within the framework of a simple time-dependent oscillator model. Turn-on delay and uncertainty (jitter) of comparator switching times are analysed taking into account the influence of thermal fluctuations and the finite time duration of clock pulse. Restrictions on speed performance of RSFQ cells caused by both times are considered. Some practical recommendations on the clock frequency increase are also discussed.
We have applied the Langevin-Heisenberg-Lax formalism for dissipative quantum systems to a balanced Josephson junction comparator operating as a fast, single-shot detector of state of a flux (rf-SQUID) qubit. Earlier experiments and theoretical analysis have shown that such a detector may reach quantum- limited resolution when it measures signal from a high-impedance (current) source. In this work, we have calculated the flux resolution of a detector for a signal source with finite inductive impedance (e.g., a flux qubit) for both an instant switching of the comparator, and for its switching with a realistic SFQ driver. The results show that the flux resolution may be quite high: for typical experimental parameters, the signal-to-noise ratio may be on the order of 10, at 10-ps-scale measurement time. Moreover, the natural energy measure of the resolution, Eout, may be made (within a narrow range of parameters) smaller than planck/2. This situation is similar to the case of continuous flux measurements using SQUIDs. In both cases, a more adequate sensitivity measure requires an account of the fluctuation back-action of the detector on the signal source. In this work we have shown that in the case of single-shot measurements, the back-action effects as characterized by the "information/dephasing" measure, may be brought down to their fundamental limit by at least two methods: coupling quenching and feedback compensation.