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Moscow University Physics Bulletin

The Influence of the McCumber Parameter on Parametric Amplification of High-Frequency Radiation by Josephson Junctions

В. Ч. Жуковский, Позднякова Олеся Дмитриевна, В. Д. Кревчик, Михаил Борисович Семенов, A. V. Shorokhov

Published Mar 1, 2018• 1 citation
Publisher

Abstract

The influence of the internal capacity of a Josephson junction on the parametric amplification of external electromagnetic radiation was studied in terms of a resistively and capacitively shunted junction model. The influence of the McCumber parameter on parametric amplification was clarified. It is shown that the additional regions of amplification can occur near subharmonic Shapiro steps in the case of Josephson junctions with internal capacity.

DOI
10.3103/s0027134918020169

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The influence of the internal capacity of a Josephson junction on the parametric amplification of external electromagnetic radiation was studied in terms of a resistively and capacitively shunted junction model. The influence of the McCumber parameter on parametric amplification was clarified. It is shown that the additional regions of amplification can occur near subharmonic Shapiro steps in the case of Josephson junctions with internal capacity.
Abstract Parametric amplification of a high-frequency radiation by point-like Josephson junctions in the cavity has been studied within a resistive model. It is shown numerically and analytically that near the subharmonic steps of the current–voltage characteristic there are areas of amplification of electromagnetic radiation. An one-dimensional array of the Josephson point junctions connected in series is treated. It is shown that the junctions in the array near the subharmonic steps of current–voltage characteristic are nonsynchronized and, accordingly, the amplification regions near the subharmonic steps of the array are missing.
Our observation of 1−mm wavelength radiation generated in a cavity containing a Josephson junction provides evidence for a negative effective microwave resistance in the Josephson junction, and for parametric amplification in the reflection mode by the Josephson junction. These parametric oscillations were observed at wavelengths corresponding to cavity resonances between 1.1− and 2−mm wavelength. The frequency of the emitted radiation differed from the frequency given by ν=2eV/h, and thus the radiation was not simply from the ac Josephson effect. We develop a theory that predicts a negative microwave resistance at junction bias voltages just below a cavity−induced step for resistively shunted junction, and just above the cavity−induced step for a junction with sufficient shunt capacitance. Our observations are consistent with the theory.
We study an effect of external radiation on the dynamics of Josephson junction shunted by an LC circuit. When the Josephson frequency is equal to the frequency of the circuit, additional stable resonant circuit branches appear in the IV -characteristic of the junction. The branches occur on the stable side of a narrow resonance peak, while the other peak side has a negative slope and is unstable. We show that the amplitude dependence of the Shapiro step width crucially changes when the Shapiro step is on the resonant circuit branch. These effects might give very important advantages for methods and technologies that exploit the response of Josephson junctions to microwave fields.
The effect of external radiation on the phase dynamics of Josephson junctions shunted by an LC circuit is examined. It is shown that additional resonant circuit (rc) branches appear in the current voltage characteristics of the junctions when the Josephson frequency is equal to the frequency of the formed resonance circuit. We show that the amplitude dependence of the Shapiro step width crucially changes when the Shapiro step is on the rc-branch in comparison to the case of Josephson junction without shunt. The experimental implementation of these effects might give very important advantages for existing methods and technologies.
A Josephson junction 1.6 mm wavelength microwave source has been used to demonstrate the parametric amplification by reflection necessary to maintain parametric oscillations at 1.6 mm wavelength. A perturbation calculation based on the resistively and capacitively shunted Josephson junction model gives a negative effective microwave resistance for a junction biased at voltages higher than the voltage for a cavity induced step. The parametric oscillation was observed at voltages consistent with the region in which negative resistance was calculated.