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.
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.
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 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, 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. 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. 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) 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.
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 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.
Several models, both static and dynamic, for calculating the maximum dc Josephson current versus external magnetic field “characteristic” of tunnel junctions of various geometries are described. The static models have the advantage of short computation times; the dynamic models, although slower, yield additional information on circuit-switching times. The dependence of the characteristics on the junction shape is described. The accuracy of a one-dimensional approximation used in the models has been tested experimentally, and theoretically against a two-dimensional approximation. In both cases, the one-dimensional treatment yields quantitatively good agreement provided the inductance of the junction is included in the model. Junctions defined by an oxide “window” of sinusoidal shape (maximum and minimum width at the center and ends, respectively) have a characteristic in which the side lobes are almost completely suppressed. The characteristics of a wide variety of junction shapes, including interferometers having two or more junctions, have been accurately calculated, permitting the design of devices for specific purposes.
A superconducting quantum interference grating (SQUIG), consisting of many Josephson junctions in parallel, exhibits quantum interference analogous to the optical interference pattern produced by a diffraction grating, just as the dc SQUID is the magnetic analog of the double slit in optics. The field- dependent critical current of a SQUIG with sufficiently low inductance exhibits a series of sharp peaks, similar to the position-dependent intensity of a multiple-slit interference pattern. Such a device has the potential for improved sensitivity as a magnetic sensor because of its enhanced flux-to-voltage transfer coefficient. The behavior is quite different, however, when the inductance is large. In this limit, the field-dependent critical current becomes extremely hysteretic and exhibits self- organized phase coherence, in which a peak in the critical current (indicating coherence of the junction phases) is observed after each reversal of the field sweep. We have observed this phenomenon in large inductance arrays with up to ten YBa2Cu3O7 (YBCO) bi-crystal grain boundary junctions in parallel. We have modeled the behavior using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance. According to our model calculations, self-organized phase coherence occurs when the system relaxes from its critical state, causing the phases to simultaneously relax to minima in the periodic potential representing the Josephson coupling energy, and thus to become coherent modulo 2(pi) .