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Journal of Applied Physics

Parametric amplification by unbiased Josephson junctions

M. J. Feldman, P. T. Parrish, R. Y. Chiao

Published Sep 1, 1975• 93 citations
Publisher

Abstract

The theory of parametric amplification by a series of unbiased Josephson junctions is presented. The various regimes of operation are explored. This device is in many ways different from the usual varactor parametric amplifier. In particular, a very small pump power is required and a large bandwidth is obtained. Comparison with experimental data is made.

DOI
10.1063/1.322157

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arXiv:1605.00539•Comptes Rendus Physique•Aug 1, 2016•167 citations
The theory of parametric amplification by a series of unbiased Josephson junctions is presented. The various regimes of operation are explored. This device is in many ways different from the usual varactor parametric amplifier. In particular, a very small pump power is required and a large bandwidth is obtained. Comparison with experimental data is made.
An analysis is presented describing four-photon parametric amplification in an unbiased Josephson junction. Central to the theory is the model of the Josephson effect as a nonlinear inductance. Linear, small signal analysis is applied to the « two fluid » model of the Josephson junction. The gain, gain-bandwidth product, high frequency limit and effective noise temperature is calculated for a cavity reflection amplifier. The analysis is extended to multiple (series-connected) junctions and sub-harmonic pumping.
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.
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.
We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is encoded in a specific microscopic pattern of density waves and phase excitations that can be addressed within the experimental cold-atom capabilities. This work paves the way for tunable amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing. At the same time, our analysis provides the microscopic explanation of the general notion of parametric amplification occurring in nonlinear coherent devices.
This short and opinionated review starts with the concept of quantum signals at microwave frequencies and focuses on the principle of linear parametric amplification. This process emerges from the dispersive nonlinearity of Josephson junctions driven with appropriate tones. We discuss two defining characteristics of the corresponding amplifying devices: i) the number of modes excited by the signal, idler and pump waves and ii) the number of independent ports through which these waves enter into the circuit.