Modern Aspects of Josephson Dynamics and Superconductivity Electronics

The first chapter of the book is devoted to the basics of Josephson effect. Calculations of Josephson current using different approaches are presented. Results of anisotropy and multiband effects of superconducting state on Josephson current presented in second section. Experimental fabrication parameters of Josephson junctions (JJs) and study their current-phase relation (CPR) are discussed in the third section. Dynamical properties of JJ comes next. Influence of anharmonic CPR on Josephson dynamics included in fifth section. The last section of this chapter deals with macroscopic quantum effects in JJs.

In this chapter we present results of achievement of modern analog superconducting electronics. In first section we discuss physical foundation and characteristics of superconducting edge bolometers. The influence of HTS materials on the characteristics is analyzed. Second section deals with description of samplers based on JJs. Two types of comparators-on single junction and balanced comparators are discussed. Presented results of linear theory for the estimation of time resolution of JJ comparators. Comparators using RSFQ technique discussed and ultimate characteristics presented. Third section is devoted to AC and DC SQUID magnetometers. Firstly, single and two-junction interferometers, the influence of d-wave order parameter symmetry on the characteristics are described. Furthermore, using these interferometers as sensitive elements of SQUIDs and characteristics is presented. Next section devoted to description of current state of superconducting microwave devices. Last topics in this chapter are using JJs in meteorology and description of multi-terminal superconducting devices.

The third chapter of the book is devoted to digital superconducting electronics. Firstly, brief review of this research area is presented. In second section shortly described latching Josephson logic. Foundations and basic circuits of the RSFQ logic are discussed in third section. The fourth section includes recent development in timing analysis and optimization methods of RSFQ circuit.

This chapter is devoted to describe Hamilton formalism for studying superconducting quantum bits (qubits). The first section is devoted to discuss phase, charge and flux qubits separately. For the realization of qubit operations based on JJ and their application requires the mK temperature regions. As followed from Chap. 1, anharmonic character of CPR becomes important at this temperatures and as result anharmonicity must be taken into account in consideration of JJ qubits. For this reason the influence of anharmonic CPR on qubit characteristics presented in Sect. 4.2. Description of silent qubit using anharmonic CPR given in Sect. 4.3. Flux qubit based on three JJ analyzed in Sect. 4.4. Section 4.5 is devoted to adiabatic measurements and Rabi oscillations in superconducting qubits is in Sect. 4.6.

In this chapter, we present some results of chaotic behavior of JJ systems. Firstly we discuss physical foundation and characteristics of chaotic dynamics of single JJ with generalized CPR, including anharmonic effects. Influence of control parameters on the dynamics of fractal JJ are discussed in second section. In the next section of the chapter, chaotic dynamics of resistively coupled two JJ system is presented. We further explore the system parameters and focus on the regions where a higher complexity is encountered. In Sect. 5.4 it will be shown that a simpler DC-driven JJ device can generate a wide region of hyperchaos without using an AC source compared to other studies existing in the literature. By doing so, the sensitivity of superconducting devices without the negative impacts of RF-excitation is combined with the highly-chaotic regimes in order to model a device with higher unpredictability. Last section is related with the discussion of synchronization of chaos in system of JJ with resistive coupling.