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IEEE Transactions on Magnetics

Theories of the noise rise in Josephson paramps

M. J. Feldman, Mogens T. Levinsen

Published Jan 1, 1981• 29 citations
Publisher

Abstract

A physically very interesting problem is the origin of the gain-proportional noise that distinguishes the zero-voltage Josephson parametric amplifiers. Many radically different theories have been proposed to explain the disturbingly high noise outputs from these devices. Here we collect the known experimental information about the "noise rise", and discuss the various theories in light of the experimental data. We also present some incompletely developed basic ideas which combine aspects of and expand upon the most successful of these theories.

DOI
10.1109/tmag.1981.1060895

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A physically very interesting problem is the origin of the gain-proportional noise that distinguishes the zero-voltage Josephson parametric amplifiers. Many radically different theories have been proposed to explain the disturbingly high noise outputs from these devices. Here we collect the known experimental information about the "noise rise", and discuss the various theories in light of the experimental data. We also present some incompletely developed basic ideas which combine aspects of and expand upon the most successful of these theories.
We describe a novel noise mechanism which should effect all externally pumped parametric amplifiers. The theory is developed specifically for the four-wave Josephson paramp. We predict a noise temperature rising in direct proportion to the amplifier gain; this prediction agrees perfectly with all previously published data for both the three- and four- wave Josephson amplifiers. An explicit expression for the noise temperature of the four-wave device is derived and compared to previous experiments.
Using methods from dynamical-systems theory, we reexamine the anomalous noise rise that has plagued Josephson-junction parametric amplifiers, devices potentially important for astrophysical measurements in the microwave regime. Our theory explains the puzzling gain-dependent noise temperature, and leads to new predictions which can be readily tested by experiments. Our explanation is based on a general theory of noise sensitivity near simple bifurcations: Thus, the same phenomenon should occur in other parametric amplifiers, e.g., those employing semiconductor lasers.
We take a new look at an old problem; namely, the observed ‘‘noise rise’’ in superconducting Josephson junction parametric amplifiers. By exploiting recent insights from dynamical systems theory, we show how the interplay or random noise and (nonchaotic) deterministic dynamics can result in a noise rise like that observed in experiments. Our analysis leads to a universal first-order equation which applies to all similar systems in the high-gain regime. We propose several predictions which can be tested experimentally, including that a similar noise rise should occur in modulated semiconductor injection lasers. We also analyze a previously unknown mode of operation—a ‘‘six-photon’’ mode associated with a symmetry breaking bifurcation—and discuss its potential advantages over the previously studied three- and four-photon modes.
The high-frequency amplification properties of transformer coupled, resistively shunted Josephson tunnel junctions have been investigated. The importance of the shunt loop inductance is stressed. It allows a high cutoff frequency, of significance for good high-frequency performance. The self-pumped parametric amplifier showed none of the excessive noise rise, which has hitherto plagued the development of externally pumped Josephson junction amplifiers. Around 10 GHz, we estimated a noise temperature less than 30 K for an amplifier pumped by a Josephson oscillation with a frequency well above twice the signal frequency. The corresponding gain of 5 dB may be increased in a better impedance matched circuit. The gain was very stable against variations in the bias conditions. A gain-bandwidth product as high as 0.3 was registered. The experimental results agreed well with the established theory for self-pumped parametric Josephson amplifiers. It should be possible to extend the low noise amplification by this device to mm wave frequencies. A relaxation oscillation occurred at a subharmonic of the Josephson frequency when the shunt loop inductance became large. The amplification in this mode followed closely the predictions of a simple model, where the signal modulated the switching of the sawtooth-like (relatively low frequency) relaxation current. Gains of about 15 dB were measured around 10 GHz, but the amplification was sensitive to bias conditions and noisy in this case where the relaxation frequency fell well below the signal frequency. Much improved properties were registered when the inductance was decreased so that the relaxation frequency approached the Josephson frequency and exceeded twice the signal frequency. The behavior then resembled that of a Josephson mode parametric amplifier, but the high content of harmonics of a relaxation oscillation meant that the amplifier became noisier due to converted noise from the many idler frequencies.
In superconducting quantum computing, qubit state information is conveyed via low-power microwave fields. As such, ultralow-noise microwave amplification plays a central role in measuring these fields to quickly and accurately infer the qubit state. To this end, parametric amplification, once a well-known concept for low-noise amplifiers during the 1960s and 1970s, has become the leading technology for enabling highly efficient microwave measurements of these quantum circuits. While current research efforts have elements in common with much earlier work, there are some important differences that distinguish this new generation of amplifiers. Here, we try to give an overview of what this excitement is about, how these devices work, and where there are opportunities for improvement.