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Journal of Applied Physics

Interference filter properties of nonuniform Josephson junction arrays

Morvan C. Salez, Faouzi M. Boussaha, L. Loukitch, Jean-Guy Caputo

Published Oct 15, 2007• 8 citations
Publisher

Abstract

We experimentally and numerically study the zero-voltage supercurrent versus magnetic field of nonuniform arrays of Josephson junctions parallel-connected by a superconducting stripline. The measured curves are complex, geometry-dependent, and in excellent agreement with numerical simulations using a specially developed model. Such arrays can be optimized to have specific interference patterns, suited for applications in magnetometery, quasiparticle microwave sensors, Josephson oscillators, and superconducting electronics.

DOI
10.1063/1.2796108

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We experimentally and numerically study the zero-voltage supercurrent versus magnetic field of nonuniform arrays of Josephson junctions parallel-connected by a superconducting stripline. The measured curves are complex, geometry-dependent, and in excellent agreement with numerical simulations using a specially developed model. Such arrays can be optimized to have specific interference patterns, suited for applications in magnetometery, quasiparticle microwave sensors, Josephson oscillators, and superconducting electronics.
We study experimentally and numerically the zero-voltage supercurrent vs. magnetic field of non-uniform arrays of Josephson junctions parallel-connected by a superconducting stripline. The measured curves are complex, unique and in excellent agreement with numerical simulations using a specially developed model. Using this, we can optimize the arrays to have any desired interference pattern. Such new devices could find applications in magnetometry, quasiparticle mixers and detectors, flux-flow oscillators and superconducting electronics.
Abstract : We have fabricated and tested large scale arrays of Josephson junctions. Some devices have as many as 150,000 junctions in a single device. To aid in device design we have also developed a numerical simulation program in Matlab to simulate voltage magnetic field characteristics for these arrays. Our numerical simulation code supports the modeling of 2 dimensional array structures and takes into account mutual interactions between all of the squids in the array. The results are in excellent agreement with our experimental measurements. We have also performed measurements of the critical current noise in our Josephson junctions and have been testing arrays in flux locked loops.
A model for describing the interference and diffraction of wave functions of one-dimensional Josephson array interferometers is presented. The derived expression for critical current modulations accounts for an arbitrary number of square junctions, the variable distance between these, and the variable size of their area. Predictions are tested on real arrays containing up to 20 equally spaced and identical junctions and on arrays shaped with peculiar geometries. A very good agreement with the modulations predicted by the model and the experimental results is obtained for all the tested configurations. It is shown that specific designs of the arrays generate significant differences in their static and dynamical (non-zero voltage) properties. The results demonstrate that the magnetic field dependence of Josephson supercurrents shows how interference and diffraction of macroscopic quantum wavefunctions can be manipulated and controlled.
We present experimental results on the magnetic field B dependent voltage response V(B) of a number of N resistively shunted Josephson junctions connected in parallel by a multiple loop network. For an appropriate distribution of the array loop sizes, such networks constitute superconducting quantum interference filters (SQIFs) with voltage response functions V(B) that are not /spl Phi//sub 0/-periodic. The voltage response of SQIFs is a unique function around a global minimum at B=0 that has a high sensitivity and a low noise level. In contrast to conventional superconducting quantum interference devices, SQIFs can be directly employed as highly sensitive magnetometers allowing the absolute measurement of magnetic fields. The experimental results are in very good agreement with the theoretical predictions on which basis the SQIF has been fabricated, All findings suggest that superconducting quantum interference filters may allow the design of novel superconducting devices.
A theoretical study is presented for a number N of Josephson junctions connected as a one-dimensional (1D) parallel array in such a manner that there are $N\ensuremath{-}1$ individual superconducting loops with arbitrary shape formed. In the resistive array mode, for bias currents I>Ic,I>{I}_{c},I>Ic​, all Josephson junctions in the array oscillate at the same magnetic field dependent frequency ${\ensuremath{\nu}}_{B}$ which is, in general, not a ${\ensuremath{\Phi}}_{0}\ensuremath{-}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{c}$ function of the strength of magnetic field B.\mathbf{B}.B. Within the range of validity of the resistively and capacitively shunted junction (RCSJ) model the periodicity of ${\ensuremath{\nu}}_{B}$ is controlled by the array geometry alone and does not depend on the distribution of the array junction parameters. In the overdamped junction regime, ${\ensuremath{\nu}}_{B}$ is for certain types of unconventional grating structures a unique function around a sharp global minimum at B=0.\mathbf{B}=0.B=0. This filter property does not apply for regular gratings and superconducting quantum interference devices (SQUID's). Computer simulations of the full nonlinear array dynamics reveal that the qualitative macroscopic quantum interference properties of unconventional arrays are governed, irrespective of the strength of inductive couplings, by a complex structure factor SN(B){S}_{N}(\mathbf{B})SN​(B) which can be determined analytically. Also, the performance of magnetometers based on 1D arrays with unconventional grating structure can be significantly better than the performance of conventional SQUID's. In particular, 1D arrays with unconventional grating structure should provide a technically rather unsophisticated precision measurement of absolute strength and orientation of external magnetic fields.
In this paper we discuss the influence of the DC biasing circuit on operation of parallel biased quasioptical Josephson junction oscillator arrays. Because of nonuniform distribution of the DC biasing current along the length of the bias lines, there is a nonuniform distribution of magnetic flux in superconducting loops connecting every two junctions of the array. These DC self-field effects determine the state of the array. We present analysis and time-domain numerical simulations of these states for four biasing configurations. We find conditions for the in-phase states with maximum power output. We compare arrays with small and large inductances and determine the low inductance limit for nearly-in-phase array operation. We show how arrays can be steered in H-plane using the externally applied DC magnetic field.