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arXiv:cond-mat/0411237 · Journal of Applied Physics

Giant relaxation oscillations in a very strongly hysteretic superconductive quantum interference device ring-tank circuit system

Terrence D. Clark, Robert J. Prance, R. Whiteman, Helen Prance, M. J. Everitt, Adi R. Bulsara, Jason F. Ralph

Published Sep 15, 2001• 3 citations
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Abstract

In this article, we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic superconducting quantum interference device (SQUID) ring, coupled to a rf tank circuit resonator, display relaxation oscillations. We demonstrate that the overall form of these characteristics, together with the relaxation oscillations, can be modeled accurately by solving the quasiclassical nonlinear equations of motion for the system. We suggest that in these very strongly hysteretic regimes, SQUID ring-resonator systems may find application in logic and memory devices.

DOI
10.1063/1.1398594

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In this article, we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic superconducting quantum interference device (SQUID) ring, coupled to a rf tank circuit resonator, display relaxation oscillations. We demonstrate that the overall form of these characteristics, together with the relaxation oscillations, can be modeled accurately by solving the quasiclassical nonlinear equations of motion for the system. We suggest that in these very strongly hysteretic regimes, SQUID ring-resonator systems may find application in logic and memory devices.
In this paper we consider new and remarkable dynamical behavior displayed by a strongly hysteretic SQUID (Superconducting QUantum Interference device)-a single Josephson weak link enclosed by a thick superconducting ring inductively coupled to a radio frequency (rf) parallel LC tank circuit resonator. Experimentally, we show that in the strongly hysteretic regime this coupled system can display remarkable level structure in its dynamics, quite different to that normally associated with rf driven SQUID ring systems. We demonstrate theoretically that this level structure arises when the SQUID ring responds non-adiabatically to time dependent changes in its potential, i.e. so that the ring no longer stays at or very close to the minimum in this potential as it changes in time.
In this paper we study numerical solutions to the quasiclassical equations of motion for a superconducting-quantum-interference device ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g., 10 state), multilevel logic and memory.
We have measured with high accuracy (100 ppm) and high precision (5--10 ppm) the impedance of a rf-driven resistive superconducting quantum interference device (SQUID) as a function of the amplitude and frequency of the radio-frequency (rf) bias, as a function of the current bias, and as a function of several other circuit parameters. We have developed the coupled differential equations for the resistive SQUID and for the rf tank circuit. The fit of the solutions of these equations to the data for nonhysteretic junctions is excellent. We were unable to develop solutions for the hysteretic case and thus simply present examples of typical data obtained in order to illustrate the differences with the nonhysteretic case. The relationship of this study to noise thermometry using resistive SQUID's is indicated.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
We have developed a matching scheme for the operation of a rf superconducting quantum interference device (SQUID) with a lumped-element tank circuit at pumping frequencies up to 1 GHz. This conventional LC resonant circuit is inductively coupled to a matching coil, which is connected to the 50 Ω transmission line. We characterized the flux noise of high-temperature rf SQUIDs at resonant frequencies between 221 and 950 MHz. At about 900 MHz, we obtained the white flux noise of about 14.6 μφ0/Hz with a SQUID inductance LS=150 pH and 20 μφ0/Hz with LS=260 pH. Several of such tank circuits can be driven in parallel or in series with only one cable.
In order to study the effect of a multiturn input coil on superconducting quantum interference device (SQUID) characteristics, the radio frequency (rf) properties of the coupling circuit between the SQUID coil and the input coil are studied. For the measurement of rf properties of the coupling circuit, the so-called expanded model of the coupling circuit using normal metals was adopted, which is shown to be very useful for this purpose. It is shown that the SQUID coil cannot be expressed by a simple inductance when the SQUID coil is coupled to the input coil, i.e., many resonant structures are observed in rf properties of the coupling circuit. It is also shown that the damping resistance is useful in suppressing the resonant structures. Using the experimental results, a circuit model of the SQUID coupled to the multiturn input coil is proposed.