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Physical review. B, Condensed matter

Noise rise in parametric amplifiers

Paul H. Bryant, Kurt A. Wiesenfeld, Bruce McNamara

Published Jul 1, 1987• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.36.752

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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.

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arXiv:1406.0197•Scientific Reports•Feb 20, 2012•16 citations
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.
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.
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.
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.
A comprehensive account of the theory of the singly quasidegenerate Josephson junction parametric amplifier is given. In this mode the signal and idler frequencies are both approximately equal to half the pump frequency, and hence the signal and idler channels have a common termination. It is shown that the performance of the amplifier characterized by properties such as gain-bandwidth product, noise temperature, and saturation depends strongly on the embedding microwave circuit. In particular any uncompensated series reactance may deteriorate the overall performance. Internal shot and Johnson noise as well as incident thermal radiation is included in the discussion. It is shown that the noise temperature is virtually independent of noise injected from external sources and that minimum noise temperature is automatically achieved if the amplifier is tuned to maximize the gain-bandwidth product. The analytical results are illustrated by self-consistent numerical solutions of the circuit equations.
The fundamental noise limit of a phase-preserving amplifier at frequency [Formula: see text] is the standard quantum limit [Formula: see text]. In the microwave range, the best candidates have been amplifiers based on superconducting quantum interference devices (reaching the noise temperature [Formula: see text] at 700 MHz), and non-degenerate parametric amplifiers (reaching noise levels close to the quantum limit [Formula: see text] at 8 GHz). We introduce a new type of an amplifier based on the negative resistance of a selectively damped Josephson junction. Noise performance of our amplifier is limited by mixing of quantum noise from Josephson oscillation regime down to the signal frequency. Measurements yield nearly quantum-limited operation, [Formula: see text] at 2.8 GHz, owing to self-organization of the working point. Simulations describe the characteristics of our device well and indicate potential for wide bandwidth operation.