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arXiv:quant-ph/0207082 · Physical Review Letters

Quantum Fluctuations in Josephson Junction Comparators

Thomas J. Walls, Timur V. Filippov, Konstantin K. Likharev

Published Nov 5, 2002• 33 citations
arXivHTMLPDF

Abstract

We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.

DOI
10.1103/physrevlett.89.217004

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We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.
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.
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The Josephson balanced comparator, a decision-making circuit comprising two Josephson junctions (JJs) connected in series from a clocking perspective and in parallel for the current to be measured, is ubiquitous in single flux quantum (SFQ) logic. Its noise properties are crucial for the performance of logic devices. The characteristics of the balanced comparator can also be used to monitor fab process and design implementation as an indicator for excess noise, overheating, linearity, dynamic effects, etc. We designed several test structures to measure gray zone of various comparators fabricated in different nodes of process at MIT-LL. We used digital circuitry to measure comparator characteristics at low frequencies and an analog testbed to perform high frequency characterization. Experimental results for gray zone of comparators designed for fabrication nodes with different current densities, sheet resistances, critical damping are presented and studied as a function of clock frequency.
We consider quantum fluctuations in a current biased overdamped Josephson junction in the regime when the bias current is larger than the critical current. The fluctuations of the voltage and phase across the junction are assumed to be initiated by equilibrium current fluctuations in the shunting resistor. This corresponds to low enough temperatures, when fluctuations of the normal current in the junction itself can be neglected. Quantum effects are important when the resistor temperature is low compared to the Josephson frequency, even in the case when noise is measured at frequencies lower than the temperature. We used the quantum Langevin equation in terms of random variables related to the limit cycle of the nonlinear Josephson oscillator. This allows to go beyond the perturbation theory and calculate the widths of the Josephson radiation lines.
We developed a weak-linked Josephson junction time-domain simulation tool based on the Bardeen-Cooper-Schrieffer (BCS) theory to account for the electrodynamics of Cooper pairs and quasiparticles in the presence of thermal noise. The model, based on Werthamer and Harris formalisms, allows us to describe the behavior of Josephson junctions for various current and/or voltage input waveforms, analog or digital, and for any operating temperature below the critical temperature of the superconducting materials. We show a good agreement between experimental and simulated IV curves of Josephson junctions, as well as a relative increase of the grey zone width of an SFQ balanced comparator between 4 and 20% due to the presence of quasiparticles, for McCumber parameters comprised between 0.1 and 1, respectively.
The Josephson balanced comparator is the key component of Single Flux Quantum logic devices because it is the decision making element. It is formed by two Josephson junctions (JJs) connected in series from a clocking perspective and in parallel for the current to be measured. Its noise properties are crucial for the performance of logic devices. The balanced comparator can also be used to monitor the fab process and design implementation as an indicator of excess noise, overheating, linearity, dynamic effects, etc. We designed several test structures to measure the comparator gray zone at different fabrication process nodes at MIT-LL. We used digital circuitry to measure comparator characteristics at low frequencies. An analog testbed was used to perform high-frequency characterization. Experimental results for different current densities, sheet resistances, damping and clock frequencies are presented.