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Journal of Modern Physics

Quantum Interference in Josephson Junctions

Roberto De Luca

Published Jan 1, 2015• 6 citations
Publisher

Abstract

The parallelism between diffraction and interference in optics and quantum interference in Josephson junctions is discussed and studied in details. The interdisciplinary character of the present work is highlighted through specific examples. The Fraunhofer-like pattern of the maximum Josephson current in a single Josephson junction and the periodic field dependence of the critical current in two-junction and in multi-junction quantum interferometers is analyzed and discussed in comparison with the homologous classical optical phenomena.

DOI
10.4236/jmp.2015.65057

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The parallelism between diffraction and interference in optics and quantum interference in Josephson junctions is discussed and studied in details. The interdisciplinary character of the present work is highlighted through specific examples. The Fraunhofer-like pattern of the maximum Josephson current in a single Josephson junction and the periodic field dependence of the critical current in two-junction and in multi-junction quantum interferometers is analyzed and discussed in comparison with the homologous classical optical phenomena.
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.
Driven atomic Josephson junctions allow one to monitor phase-coherent dynamics with unprecedented control and flexibility of the system's physical conditions. While cold-atom manifestations of the Josephson effect have been extensively studied in a wide variety of settings, atomic Josephson junctions in synthetic electromagnetic fields remain largely unexplored. Here, we show that synthetic magnetic fields can induce Fraunhofer-like modulations of the critical current in atomic Josephson junctions. Although this effect presents analogies to the Fraunhofer patterns found in superconducting devices, distinctive features emerge due to the neutral nature of the superfluid. We investigate the underlying spatial interference mechanisms and elucidate the role of Josephson vortices in the formation of spatially modulated current distributions based on numerical simulations. Our results open up new avenues for matter-wave circuits to deepen our understanding of spatial coherence in Josephson junctions, which are fundamental to the development of novel quantum technologies.
A single-junction superconducting quantum interferometer with external high-frequency excitation is considered, in which the weak coupling is described within the framework of the resistive model. An analysis for the hysteresis-free state serves to define the parameters characterizing the Josephson junction, including the current as a function of the phase difference at the junction, as well as the interference term in the dissipative component of the current. The theoretical results are compared with experiment to define certain parameters of the Josephson junction and the sign of the interference term.
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.
Complex chaotic and stochastic phenomena in single-junction and double-junction superconducting quantum interferometers are studied with the help of specially designed high-speed analog circuit. In Contrast with the earlier versions of the Josephson junction analogs, the digital integrated circuits with the voltage-controlled time delay have been used as the basic elements of the circuit, which has enabled us to extend its frequency range up to 1OO KHz. Of the phenomena studied with the analog, two are discussed in detail: i. For the single-junction interferometer under the periodic external drive the region of parameters is found, where the device exhibits complex and chaotic behavior and thus cannot be used in parametric amplifiers and ac SQUIDs. The boundary of the chaotic behavior region is found to be very close to that predicted from a very simple criterion, ii. For the double-junction interferometer, we have measured the probability of the establishing the basic ("0-th") static state as a result of a slow decrease of the bias current, as a function of the interferometer parameters. The region is determined where the probability is very close to unity, and the interferometer can be used as an NDRO memory cell.