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Applied Physics Letters

Self-Pumped Josephson Parametric Amplification

Helmut Kanter, Arnold H. Silver

Published Dec 15, 1971• 35 citations
Publisher

Abstract

Parametric gain has been demonstrated at 30 MHz using the nonlinear inductance of Josephson point-contact devices. SQUID-type configurations were used to achieve degenerate-mode negative-resistance amplification with self-pumping achieved via the internal Josephson oscillations. Gain as large as 11 dB was measured. The small-signal analysis predicts parametric amplification and delineates the importance of the critical current, circuit loss, and circuit coupling efficiency.

DOI
10.1063/1.1653795

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IEEE Transactions on Magnetics•Jan 1, 1977•16 citations
Parametric gain has been demonstrated at 30 MHz using the nonlinear inductance of Josephson point-contact devices. SQUID-type configurations were used to achieve degenerate-mode negative-resistance amplification with self-pumping achieved via the internal Josephson oscillations. Gain as large as 11 dB was measured. The small-signal analysis predicts parametric amplification and delineates the importance of the critical current, circuit loss, and circuit coupling efficiency.
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 developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of eight superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude gain $\ifmmode\times\else\texttimes\fi{}$ bandwidth above 60 MHz, and a 1 dB compression point of $\ensuremath{-}123$ dBm at 20 dB gain are obtained in the nondegenerate mode of operation. Phase-sensitive amplification-deamplification is also measured in the degenerate mode and yields a maximum gain of 37 dB. The compression point obtained is 18 dB above what would be obtained with a single SQUID of the same inductance, due to the smaller nonlinearity of the SQUID array.
A self-pumped Josephson junction can be operated in a mode which is described in first order by a two-idler parametric amplifier analysis for a sinusoidal elastance variation. Thus the analysis and operation follows the two-idler negative resistance behavior predicted by Penfield and Rafuse for varactor diodes. Experimental observations on parametric negative conductance excitations at 9 GHz by a Josephson point contact are readily explained by the two-idler model. A total signal power gain of 12 dB was achieved with an experimental device consisting of a niobium titanium point contact in a shallow rectangular cavity coupled through a room-temperature circulator.
A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the “pumpistor.” Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, for which it becomes necessary to consider idler tones that occur. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.
We have studied the parametric amplification properties of an internally pumped Josephson tunnel junction, where the shunt contained resistive and inductive components. The amplification was, in this case, limited by circuit component values to less than 8 dB at 10 GHz, but it was very stable against variations in bias conditions. The amplifier gain-bandwidth product was large and the noise level very low. We estimated the noise temperature to be less than 50 K, which should make the device attractive for mm-wave amplification.
Gain and noise properties of a non-degenerate one-frequency parametric amplifier using a self-pumped Josephson junction are investigated both theoretically and experimentally. The amplifier uses the phenomenon of microwave negative resistance of the junction. Theoretical analysis made in usual resistively shunted junction (RSJ) model shows that the minimum noise temperature is equal to approximately 42T. It takes place at a signal frequency f close to the junction characteristic frequency f0. Maximum effectivity (the product of the square root of power gain and relative bandwidth) can reach 0.4 at f≃f0. Gain up to 20 dB was obtained at X-band using amplifier with Nb-Ta point-contact junction. Minimum noise temperature at T = 4.2K was about 200K.