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Journal of Applied Physics

Resonant modes in Nb baselayer interferometers with two Josephson junctions

Gianfranco Paternò, Anna Maria Cucolo, G. Modestino

Published Mar 1, 1985• 11 citations
Publisher

Abstract

Resonances in the current-voltage characteristics of interferometers with two Nb-NbOx-Pb window junctions have been experimentally investigated. The data are compared with the theoretical curves computed both for the voltage and for the magnetic field dependence of the resonance amplitudes. Very good agreement is found in all the range of values of the damping parameter Γ=I0 R/Vr, where Vr is the resonant voltage and I0 and R are the maximum Josephson current and the parallel resistance of each junction. New features that cannot be explained in terms of the existing theory have been observed in devices with larger values of the parameter β=2πLI0/Φ0, where L is the loop inductance, and Φ0 is the flux quantum.

DOI
10.1063/1.334437

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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.

Physical review. B, Condensed matter•Jul 1, 1982•117 citations
Resonances in the current-voltage characteristics of interferometers with two Nb-NbOx-Pb window junctions have been experimentally investigated. The data are compared with the theoretical curves computed both for the voltage and for the magnetic field dependence of the resonance amplitudes. Very good agreement is found in all the range of values of the damping parameter Γ=I0 R/Vr, where Vr is the resonant voltage and I0 and R are the maximum Josephson current and the parallel resistance of each junction. New features that cannot be explained in terms of the existing theory have been observed in devices with larger values of the parameter β=2πLI0/Φ0, where L is the loop inductance, and Φ0 is the flux quantum.
Planar interferometers with two Nb-NbOx-Pbln functions have been fabricated. Because of the peculiar configuration adopted, both a symmetric and an asymmetric current bias are possible on the same sample. The loop area is on a plane perpendicular to the cross section of the functions, and, therefore, the flux coupled to them is negligible. ThreshoM curves have been measured for different values of the characteristic parameter fl = LI1/qbo, where 1i and L are the maximum Josephson current and the inductance of the interferometer and C~o is the flux quantum. The dependence of the current modulation depth upon fl has been also investigated. A comparison of the experimental data with the theory shows quantitative agreement.
Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.
The high frequency properties of the one-dimensional transmission line consisting of a parallel array of resistively shunted Josephson tunnel junctions have been studied in the limit of relatively low damping where this nonlinear system exhibits new and interesting phenomena. Here we report on experimental and numerical investigations of a resonant step observed at a voltage corresponding to 600 GHz in the dc current-voltage characteristic of a parallel array of 20 identical small NbAl2O3Nb Josephson junctions interconnected by short sections of superconducting microstrip line. The junctions are mutually phase locked due to collective interaction with the line sections excited close to the half wavelength resonance. The phase locking range can be adjusted by means of an external dc magnetic field and the step size varies periodically with the magnetic field. The largest step corresponds to a superconducting phase difference of π between neighboring junctions.
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.