We have calculated the total critical current as a function of applied magnetic flux for a superconducting interferometer consisting of many Josephson junctions in parallel. An enhancement and narrowing of the periodic principal maxima in the critical current versus flux characteristic is predicted as the number of junctions in parallel increases, even when the effects of finite self- and mutual inductances and nonuniformity of the junction critical currents are included in the calculations. The possible application of the superconducting quantum interference grating, or SQUIG, for the detection of magnetic flux is discussed.
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) .
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.