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IEEE Transactions on Magnetics

Chaotic and stochastic phenomena in superconducting quantum interferometers

Victor K. Kornev, Vasili K. Semenov

Published May 1, 1983• 14 citations
Publisher

Abstract

Complex chaotic and stochastic phenomena in single-junction and double-junction superconducting quantum interferometers are studied with the help of specially designed high-speed analog circuit. In Contrast with the earlier versions of the Josephson junction analogs, the digital integrated circuits with the voltage-controlled time delay have been used as the basic elements of the circuit, which has enabled us to extend its frequency range up to 1OO KHz. Of the phenomena studied with the analog, two are discussed in detail: i. For the single-junction interferometer under the periodic external drive the region of parameters is found, where the device exhibits complex and chaotic behavior and thus cannot be used in parametric amplifiers and ac SQUIDs. The boundary of the chaotic behavior region is found to be very close to that predicted from a very simple criterion, ii. For the double-junction interferometer, we have measured the probability of the establishing the basic ("0-th") static state as a result of a slow decrease of the bias current, as a function of the interferometer parameters. The region is determined where the probability is very close to unity, and the interferometer can be used as an NDRO memory cell.

DOI
10.1109/tmag.1983.1062476

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Complex chaotic and stochastic phenomena in single-junction and double-junction superconducting quantum interferometers are studied with the help of specially designed high-speed analog circuit. In Contrast with the earlier versions of the Josephson junction analogs, the digital integrated circuits with the voltage-controlled time delay have been used as the basic elements of the circuit, which has enabled us to extend its frequency range up to 1OO KHz. Of the phenomena studied with the analog, two are discussed in detail: i. For the single-junction interferometer under the periodic external drive the region of parameters is found, where the device exhibits complex and chaotic behavior and thus cannot be used in parametric amplifiers and ac SQUIDs. The boundary of the chaotic behavior region is found to be very close to that predicted from a very simple criterion, ii. For the double-junction interferometer, we have measured the probability of the establishing the basic ("0-th") static state as a result of a slow decrease of the bias current, as a function of the interferometer parameters. The region is determined where the probability is very close to unity, and the interferometer can be used as an NDRO memory cell.
A high-speed electronic analog for high-accuracy simulation of complex multi-Josephson-junction circuits has been developed. The analog contains only two types of special cicuits, A and B, interconnected with a simple high-frequency commutation circuit and several ordinary operational low-frequency amplifiers. With our present five-junction version of the analog, several problems of urgent interest have been solved, including those of chaos excitation in the double-junction interferometer and mutual phase locking in multi-tunnel-junction arrays.
de Broglie wave interferometers have been constructed, successfully utilizing extended superconducting links of tin to couple coherently the quantum phases of two Josephson junctions. The current transmitted by these devices was periodic in the enclosed flux (periodicity (.9 ± .3) h/2e) demonstrating unambiguously coherence of the superconducting order parameter over 1.33 meters. We may define a Josephson junction as one for which the quantum mechanical coupling energy is insufficient to overcome the disruptive effects of noise. Consequently, the relative phase of the coupled superconductors is not stabilized and the zero Josephson current fluctuates, (bandwidth ~ 2eVnoise/h) averaging to zero. Two such junctions have been coupled to an electromagnetic cavity formed by the superconducting arms of a quantum interferometer (junction separation 1. 33 meters). With an applied steady voltage such that the Josephson current excites a normal mode of the cavity, a coherent radiation field is built up. This coherent radiation feeds back to the junctions forcing time coherence on the phase precession, resulting in a dynamic stabilization of the junctions. Under these conditions a series of constant voltage has been observed in the I-V characteristic of one interferometer. The Josephson frequency associated with these steps is shown to be characteristic of the electromagnetic resonant modes of the cavity. Frequency modulation analysis, combined with a detailed analysis of the cavity-junction combination, predicts such maxima in the tunneling of pairs when a selection rule, (m + n) even, is obeyed. Here m/2 is the number of flux quanta (h/2e) linking the interferometer and n is the order of the cavity resonance excited. Experimental confirmation of the detailed predictions of the analysis is presented.
We have developed a cell library for superconducting large scale integrated (LSI) digital circuits based on Single Flux Quantum (SFQ) devices. The circuits were designed for a 6-kA/cm2Nb/AlOx/Nb junction process with 10 mask levels including one ground plane and two Nb wiring layers. The initial design and optimization of the circuit parameters were achieved by means of the optimization functions in a circuit simulator, PSCAN2, to ensure that important circuit parameters, Josephson critical current (IC), bias current (Ibias), and inductance satisfied minimal margin requirements. Critical margins of ICand Ibiaswere then further improved manually. To compensate the scattering in the circuit parameters from fabrication by design as much as possible, the critical junction parameters were optimized to further centralize the IC. The library cells were laid out following our design rules determined by systematic experiments on process control monitors (PCM). Basic cells including Josephson transmission lines, splitters, confluence buffers, D flip-flops, T flip-flops, and XOR and NDRO gates were designed, fabricated, and successfully tested at low frequencies. Wide overlaps of the operating regions for the common bias voltages were confirmed.
The dc and ac Josephson effects and the behavior of the current‐voltage characteristics of Josephson junctions are briefly reviewed. The Josephson junction cryotron is described. Two cryotrons have been incorporated into a NDRO memory cell with a switching time of 80ps, a power‐delay product of 10−16J, and an area of 900μm2. DRO memory cells involving the storage of a single flux quantum have estimated switching speeds of 50ps and a dissipation in continuous operation of 40nW. Latching logic elements with a switching time of 200ps and a power‐delay product of 5fJ have been built. Non‐latching devices and the flux shuttle are described. The use of dc and rf SQUIDS in conjunction with flux transformers for magnetic measurements is discussed. Presently achieved sensitivities are: magnetic field, 10−15THz−1/2, magnetic field gradient, 10−13Tm−1Hz−1/2; magnetic susceptibility, 2×10−11 e.m.u. for 1cm3 at 10−1T; voltage, 10−15VHz−1/2. The highest energy resolution reported for a SQUID‐transformer combination is 8×10−30 JHz−1 in a frequency range from 2×10−2Hz to 1kHz. At lower frequencies the noise power spectrum is 1/f. The performance of the computer and measuring devices is compared with that of conventional (non‐superconducting) devices.
Multijunction superconducting quantum interferometers can be created spontaneously by intrinsic junctions in granular high-Tc materials, and as a by-product of step-edge technology used to fabricate high-Tc thin film dc superconducting quantum interference devices. The properties of such systems are relatively little known. The theory predicts multivalued dependence of critical current Ic on applied magnetic flux Φe and the appearance of different stationary ‘‘phase states’’ related to different possible relationships between the phases of superconducting order parameter in individual junctions. We report on the measurements performed on a (2×2) quantum interferometer, comprising a series array of two underdamped all-niobium tunnel junctions in each parallel arm. Experimental results closely follow the theoretical predictions and reveal several instability regions, in which noise generation takes place. These findings can possibly be related to the random telegraph noise observed in high-Tc materials.