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Journal of Applied Physics

High-Frequency Response of Josephson Point Contacts

Helmut Kanter, F. L. Vernon

Published Jul 1, 1972• 101 citations
Publisher

Abstract

For a current-driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high-frequency currents is calculated with a second-order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic-frequency regions depending on whether the internal self-generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0< or >ω the response could be expressed by easily observable parameters of the dc voltage-current characteristics. This permits comparison of the predictions with experimental results obtained on point-contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point-contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise-equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.

DOI
10.1063/1.1661682

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Measurements of quantum noise in resistively shunted Josephson junctions

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Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where ${I}_{0}$ is the critical current, $C$ is the junction capacitance, and ${L}_{s}$ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the ${L}_{s}C$ resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.

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Negative resistance effects with Josephson junctions

Helmut Kanter

Conventional negative resistance effects can be generated with a Josephson junction quite similar to that obtained with Varactor diodes, with the additional advantage that the internal, self-generated oscillations serve as a pump, i. e., only a dc source is needed instead of a high frequency pump source. However, another negative resistance effect typical for a Josephson junction is possible as has been predicted recently for the current controlled, highly damped junction model. The effect has recently been demonstrated experimentally at 9 GHz. Characteristically, the pump (Josephson) frequency is smaller than the frequency of the amplified signal and the pump mechanism is effective over a broad range of frequencies in contrast to the conventional parametric negative resistance effect where the pump frequency exceeds that of the signal and idler and where the frequency of operation is limited to a narrow range. The broad-band feature renders the amplifier operation uncritical to tuning and bias voltage fluctuations. The fact that the junction is the element of lowest impedance in the circuit alleviates to a degree the matching problem generally encountered with Josephson contacts. An assessment of the competitiveness of this effect in microwave technology is given.

Revue de Physique Appliquée•Jan 1, 1974•0 citations
For a current-driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high-frequency currents is calculated with a second-order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic-frequency regions depending on whether the internal self-generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0< or >ω the response could be expressed by easily observable parameters of the dc voltage-current characteristics. This permits comparison of the predictions with experimental results obtained on point-contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point-contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise-equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.
The dc characteristics of superconducting point-contact junctions subjected to external noise currents are measured under the condition that the noise-frequency spectrum is below the Josephson frequency. It is shown that the curves are in agreement with a model based on modulation of the noise-free dc characteristic. Although in the low-bias-voltage region the shape of the curves is qualitatively similar to previous theoretical predictions for the case of high-frequency noise, for higher voltages the shapes are different. Quantitative differences exist over the whole range of bias voltage.
The Josephson frequency conversion in the millimeter and submillimeter wave region is studied with superconducting Nb-Nb point contact junctions at 4.2 K, using the contact both as the local oscillator and the mixer with intermediate frequencies of 0.1 and 9.2 GHz. Frequency conversion signals are only detected in the latter case with a microwave receiver at 9.2 GHz in a range of Josephson frequencies between 145 and 1 600 GHz. The experiments with intermediate frequency fi of 0.1 GHz indicate for this small value of f i that the observed signals are not related to frequency conversion but noise effects. An analysis of the frequency conversion mechanism in a Josephson junction operated as an oscillator-mixer is proposed which includes the noise effects and also the feedback effects induced in a junction driven by a constant current source. We have then investigated the noise properties up to 450 GHz of superconducting point-contacts using the junction as an oscillator-mixer where the Josephson current is mixed with harmonics of an externally applied signal. The emitted intermediate frequency is detected at 9.2 GHz and its linewidth is measured. In the very high frequency range the dc quasiparticle current dominates in a Josephson weak-link and we compare the corresponding theoretical linewidth calculated by Scalapino with our experimental results.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.
Conventional negative resistance effects can be generated with a Josephson junction quite similar to that obtained with Varactor diodes, with the additional advantage that the internal, self-generated oscillations serve as a pump, i. e., only a dc source is needed instead of a high frequency pump source. However, another negative resistance effect typical for a Josephson junction is possible as has been predicted recently for the current controlled, highly damped junction model. The effect has recently been demonstrated experimentally at 9 GHz. Characteristically, the pump (Josephson) frequency is smaller than the frequency of the amplified signal and the pump mechanism is effective over a broad range of frequencies in contrast to the conventional parametric negative resistance effect where the pump frequency exceeds that of the signal and idler and where the frequency of operation is limited to a narrow range. The broad-band feature renders the amplifier operation uncritical to tuning and bias voltage fluctuations. The fact that the junction is the element of lowest impedance in the circuit alleviates to a degree the matching problem generally encountered with Josephson contacts. An assessment of the competitiveness of this effect in microwave technology is given.