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Physical review. B, Condensed matter

rf power dependence of subharmonic voltage spectra of two-dimensional Josephson-junction arrays

S. E. Hebboul, J. C. Garland

Published Mar 1, 1993• 25 citations
Publisher

Abstract

We have measured the rf-bias-current dependence of the \ensuremath{\nu}/2 subharmonic spectral response of planar 300\ifmmode\times\else\texttimes\fi{}300 Nb-Au-Nb proximity-coupled Josephson-junction arrays. The \ensuremath{\nu}/2 subharmonic voltage spectrum was examined at two rf-bias frequencies, \ensuremath{\nu}/${\ensuremath{\nu}}_{\mathit{c}}$\ensuremath{\approxeq}1.4, 2.0 (${\ensuremath{\nu}}_{\mathit{c}}$\ensuremath{\approxeq}120 MHz), and in applied magnetic fields corresponding to f=0,1/2 flux quantum per plaquette. The measurements were compared to analytical predictions for an rf-biased asymmetric superconducting quantum interference device with non-negligble loop inductance and large rf-bias-current amplitudes, based on the resistively shunted Josephson-junction model. Reasonable agreement was found between experiment and theory, suggesting that a possible origin for the observed subharmonic behavior in arrays involves an interplay between array plaquette inductances and junction critical-current variations.

DOI
10.1103/physrevb.47.5190

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•Jan 1, 1993•0 citations
We have measured the rf-bias-current dependence of the \ensuremath{\nu}/2 subharmonic spectral response of planar 300\ifmmode\times\else\texttimes\fi{}300 Nb-Au-Nb proximity-coupled Josephson-junction arrays. The \ensuremath{\nu}/2 subharmonic voltage spectrum was examined at two rf-bias frequencies, \ensuremath{\nu}/\ensuremathνc{\ensuremath{\nu}}_{\mathit{c}}\ensuremathνc​\ensuremath{\approxeq}1.4, 2.0 (\ensuremathνc{\ensuremath{\nu}}_{\mathit{c}}\ensuremathνc​\ensuremath{\approxeq}120 MHz), and in applied magnetic fields corresponding to f=0,1/2 flux quantum per plaquette. The measurements were compared to analytical predictions for an rf-biased asymmetric superconducting quantum interference device with non-negligble loop inductance and large rf-bias-current amplitudes, based on the resistively shunted Josephson-junction model. Reasonable agreement was found between experiment and theory, suggesting that a possible origin for the observed subharmonic behavior in arrays involves an interplay between array plaquette inductances and junction critical-current variations.
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.
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.
This paper presents the results of the measurements of 1-V Nb-AlO/sub x/-Nb, Josephson junctions arrays at temperatures 4.2-1.7 K in frequency band 54-80 GHz. The measurement of the temperature dependence of the critical current, gap voltage and subgap resistance of junctions is a useful tool for the quality control of arrays. By the measurements of the frequency dependence of array response to the microwave radiation it was found, that this response often has a resonance or interference like character, which is dependent on the array geometry. At the temperatures lower than 3-2.5 K as well as at low frequencies 54-60 GHz and T=4.2 K a transition to chaotic state of arrays was observed at small rf-power level.
Abstract Designing superconducting electronic devices involves a careful study of all the elements in the circuit, including the superconducting bias leads. In this work, we introduce a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) arrays capable of simulating the voltage-to-magnetic flux response of devices with different bias current configurations. First, we compare uniformly biased and centre biased SQUID arrays by investigating the voltage versus magnetic flux response, maximum transfer function and voltage modulation depth. Then, we calculate the time-averaged fluxoid distributions for one-dimensional (1D) and 2D centre biased arrays. Finally, we study the performance of the two bias current configurations depending on array size, screening parameter, thermal noise strength and kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D parallel SQUID arrays present an unusual voltage response caused by the asymmetric fluxoid distribution; (ii) the optimal transfer function of centre biased arrays strongly depends on the number of junctions in parallel; (iii) the performance of centre biased arrays approaches the uniform biased ones when the number of junctions in series exceeds those in parallel; (iv) while the screening parameter and the thermal noise strength clearly affect the device performance, the kinetic to self-inductance fraction seems to play only a secondary role.
The rf-power dependence of the ac-Josephson steps is measured at 720 GHz, using small area Nb tunnel junctions. This frequency is well above the gap frequency of Nb. The junction is placed in a waveguide, and connected to a superconducting stripline, which effectively tunes out the junction capacitance and facilitates the coupling of the radiation to the junction. We observe three Josephson steps, and the first step crosses the zero current axis over a considerable range of rf-power. This indicates the possible application of THz Josephson steps in voltage standards. The data are compared to the theory and we find clear evidence for the predicted intrinsic roll-off of the Josephson current amplitude above the gap frequency.