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Journal of Applied Physics

The plasma resonance in the response and in the rf impedance of a capacitively shunted Josephson junction in the presence of thermal noise

Tim Poorter, Harm Tolner

Published Dec 1, 1980• 1 citation
Publisher

Abstract

The rf impedance and the wide-band response to radiation of a resistively shunted junction (RSJ) model Josephson junction have been measured in the presence of thermal noise, using a phase-locked-loop analog of the RSJ model. In the conditions for which analytical calculations are valid there is good agreement between the theory and the analog. When the RSJ model is shunted with a capacitance, a plasma type resonance can occur in the rf impedance when the junction is biased in the supercurrent (in-lock). When thermal noise is present, this plasma resonance can also occur when a nonzero average voltage is generated across the junction. We found that in this case a resonance also occurs in the wide-band response to radiation. This resonance takes place at a frequency that can be identified as the attempt frequency, with which the junction attempts to escape the phase locked condition in which it exists for a fraction of the time even though the average voltage across the junction is nonzero. The average lifetimes of the junction in lock τin (?=0) and out of lock τout (?=?out) were also measured in the presence of thermal noise. τin is in good agreement with existing theory and τout is derived from the measurements.

DOI
10.1063/1.327618

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The rf impedance and the wide-band response to radiation of a resistively shunted junction (RSJ) model Josephson junction have been measured in the presence of thermal noise, using a phase-locked-loop analog of the RSJ model. In the conditions for which analytical calculations are valid there is good agreement between the theory and the analog. When the RSJ model is shunted with a capacitance, a plasma type resonance can occur in the rf impedance when the junction is biased in the supercurrent (in-lock). When thermal noise is present, this plasma resonance can also occur when a nonzero average voltage is generated across the junction. We found that in this case a resonance also occurs in the wide-band response to radiation. This resonance takes place at a frequency that can be identified as the attempt frequency, with which the junction attempts to escape the phase locked condition in which it exists for a fraction of the time even though the average voltage across the junction is nonzero. The average lifetimes of the junction in lock τin (?=0) and out of lock τout (?=?out) were also measured in the presence of thermal noise. τin is in good agreement with existing theory and τout is derived from the measurements.
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.
Relaxation oscillations at subharmonics of the Josephson frequency may occur in a resistively shunted superconducting tunnel junction, where the shunt loop has a large inductance. We have studied the variation in the relaxation period with the shunt inductance and resistance, the Josephson critical current, and the bias current. Steps in the current-voltage curve were noted at bias points where the subharmonic number changed. Radiation powers of the order of a nW were coupled out of small, single, tunnel junctions at 10 GHz. Linewidths scaled with the frequency square as compared with those of the Josephson mode oscillations. Wide signals centered around harmonics of the relaxation frequency were due to amplified noise. Injection locking to a fraction of the frequency of a relatively strong signal occurred, while weaker signals were amplified. Gains up to 15 dB were achieved within a fairly large bandwidth, but the noise temperature was high. The importance of parametrically up-converted noise from low idler frequencies is emphasized.
The impedance and noise of a resistive superconductive quantum interference device (R-SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R-SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R-SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R-SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.
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.
Abstract The Josephson junction (JJ) is the corner stone of superconducting electronics and quantum information processing. While the technology for fabricating low T c JJ is mature and delivers quantum circuits able to reach the “quantum supremacy”, the fabrication of reproducible and low-noise high- T c JJ is still a challenge to be taken up. Here we report on noise properties at RF frequencies of recently introduced high- T c Josephson nano-junctions fabricated by mean of a Helium ion beam focused at sub-nanometer scale on a YBa 2 Cu 3 O 7 thin film. We show that their current-voltage characteristics follow the standard Resistively-Shunted-Junction (RSJ) circuit model, and that their characteristic frequency f c = (2 e / h ) I c R n reaches ~300 GHz at low temperature. Using the “detector response” method, we evidence that the Josephson oscillation linewidth is only limited by the thermal noise in the RSJ model for temperature ranging from T ~ 20 K to 75 K. At lower temperature and for the highest He irradiation dose, the shot noise contribution must also be taken into account when approaching the tunneling regime. We conclude that these Josephson nano-junctions present the lowest noise level possible, which makes them very promising for future applications in the microwave and terahertz regimes.