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IEEE Transactions on Magnetics

Parametric properties of SQUID lattice arrays

Arnold H. Silver, David C. Pridmore-Brown, Robert D. Sandell, John P. Hurrell

Published Jan 1, 1981• 15 citations
Publisher

Abstract

Josephson junctions incorporated into microcircuit SQUIDs have many uses including digital logic and memory, parametric amplification, signal generation, and analog to digital conversion. Combining SQUIDs into coherent arrays can preserve these functions and add great flexibility in selecting power and impedance. We have investigated such general properties of the SQUID lattice array as the mode structure, dispersion relations, and stability. In particular, one unique antisymmetric mode is shown to precisely reproduce the performance of a single rf SQUID, with increased power and impedance. The application of this mode to parametric amplification has been demonstrated analytically and numerically, projecting a useful low noise amplifier with a gain of 10dB at 16% bandwidth.

DOI
10.1109/tmag.1981.1060904

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Josephson junctions incorporated into microcircuit SQUIDs have many uses including digital logic and memory, parametric amplification, signal generation, and analog to digital conversion. Combining SQUIDs into coherent arrays can preserve these functions and add great flexibility in selecting power and impedance. We have investigated such general properties of the SQUID lattice array as the mode structure, dispersion relations, and stability. In particular, one unique antisymmetric mode is shown to precisely reproduce the performance of a single rf SQUID, with increased power and impedance. The application of this mode to parametric amplification has been demonstrated analytically and numerically, projecting a useful low noise amplifier with a gain of 10dB at 16% bandwidth.
Josephson parametric amplifiers (JPAs) are key devices in superconducting quantum circuits, as they ultimately dictate quantum efficiency and speed of measurement, but they still suffer from low saturation power. This work shows that a JPA's saturation power can be increased by using a Josephson-junction array, rather than a single-junction amplifier. Modeling such an array as a nonlinear $L\phantom{\rule{0}{0ex}}C$ resonator reproduces the observed amplification and saturation effects very well. This use of arrays to fight low power saturation is easy to implement, and can be directly combined with impedance-engineered environments to enhance dynamic range even more.
This is the first Annual Report of an effort to demonstrate a low noise superconducting microwave amplifier. The amplifier is a nearly degenerate, single idler parametric amplifier which uses the nonlinear inductance of a single junction SQUID (Superconducting Quantum Interference Device). The design frequency is 9 GHz, 10 dB gain, and 16% bandwidth. In order to maximize the saturation power, the device impedance was chosen near 1ohm and a matching network was designed to transform to 50ohm. In later designs, a coherent array of SQUIDs is expected to increase the power and impedance. This report includes the design and test of the 50ohm to 1ohm broadband transformer, design and fabrication of the SQUID amplifier, and both saturation and noise analyses of the single SQUID and SQUID array. The analytical results, reported to the 1982 Applied Superconductivity Conference are: the noise temperature of the single SQUID parametric amplifier is equal to the amplifier termination temperature T(o), the response is linear to several percent of the flux quantum energy in the SQUID: the amplifier will be saturated by broad band noise if the noise source temperature is much greater than 10 To; and the array parametric amplifier has the same noise temperature as the single device indicating an N-fold increase in dynamic range. (Author)
The parametric nature of supercurrent in Josephson junctions may be exploited for amplification of high frequency signals in several modes of operation, where in each case the reactance variation is provided by the internal oscillations due to the average contact potential, a)One mode is negative resistance amplification with a single idler. This mode is entirely equivalent to that generally employed in conventional parametric amplifiers with varactor diodes. b)Negative resistance amplification with several idlers at further combination frequencies. This mode of operation is typical for the resistively shunted junction model, c)Amplification by upconversion, which is conceptually employed in the rf SQUID used in magnetometry. Experimental verifications of these various modes are described and their suitability for low noise amplification discussed. The upconverter experiment permitted the measurement of device noise by variation of the temperature of the input termination. An upper noise limit of 15°K is established. This experiment demonstrates that in high frequency application of active self-oscillating Josephson junctions the fundamental noise achievable is not greatly in excess of the thermal limit.
We have investigated the performance of a resistive rf SQUID as a 9 GHz parametric amplifier and oscillator. It was coupled to a low impedance microstrip transformer. Stable Josephson oscillations were obtained for βLQ =2eI0ZL/hf <1.1–1.8. Oscillation linewidth (830 kHz) and output power (−74 dBm) were measured. The four-photon internally pumped amplifier produced large single sideband (ssb) noise temperatures, typically around 50 K, due to the broad flanks of the pump. The best performance was achieved in the three- and four-photon externally pumped modes. Both modes gave signal gains of about 10 dB and negligible noise power contributions. A hot/cold measurement on the four-photon amplifier yielded Gdsb =13 dB (dsb=double sideband) and Tdsb =3±4 K over a bandwidth of 310 MHz. For larger values of βLQ , subharmonics 1/2 and 1/3, as well as noninteger ‘‘excitations’’ of the Josephson oscillation, were observed. The subharmonic oscillations were not tunable in frequency with unchanged linewidth. Amplification close to an excitation also produced gain but with ssb noise temperatures of ∼20 K.
TRW has been developing low noise microwave parametric amplifier with Josephson junction SQUIDs (Superconducting Quantum Interference Devices). This report summarizes the second phase of the program which includes measurement of the amplifier performance at X-band, and design and fabrication of a SQUID array amplifier. We have demonstrated gain in excess of 10 dB at 8.4 GHz and a measured noise temperature equal to 6K with an uncertainty of (+15/-7)K. Arrays with both 25 and 50 elements and 50 ohmi impedance have been designed and fabricated. These arrays should increase the dynamic range of the amplifier.
Arrays of 10 or 40 series-connected small densely packed Josephson tunnel junctions were successfully operated as parametric amplifiers at 10 GHz. Between 50 and 90% of the junctions in an array were observed to work coherently in the amplification process. Signal gain exceeding 24 dB was achieved with a pump power as low as −50 to −70 dBm. A power width (i.e., the range of the pump power for a gain within 3 dB of the peak gain) of 0.25 dB and a bandwidth of 15 MHz were measured for 20-dB gain. The power width was in accordance with theory but the bandwidth was reduced, probably due to noise saturation effects. The latter effects can be reduced by lowering the input noise temperature or by including an external band limitation. The noise temperature was also increased by saturation; however, with an external bandwidth of 60 MHz, a noise temperature of 30±20 K was measured. The application of a magnetic field has proved extremely useful as a means of tuning the amplifiers to stable high-gain operating points. This tuning was also utilized in evaluating the amplifier parameters, and the theory by Feldman, Parrish, and Chiao has been verified. The upper frequency limit for a lead tunnel junction amplifier ought to be well above 300 GHz.