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An Erratum to this paper has been published: https://doi.org/10.1134/S0021364022380039

We consider the problems related to the use of 0–π junctions with a nontrivial current–phase relation in Josephson transmission lines. The various types of excitations (fractional fluxons) propagating in such Josephson media have been studied. We have investigated the problem of the integration of Josephson transmission lines consisting of 0–π junctions (nontrivial Josephson transmission lines) with ordinary rapid single-flux-quantum electronics. We have analyzed the characteristic excitation transformation processes at the interfaces of ordinary and nontrivial Josephson transmission lines, which are largely similar to the Andreev reflections from a superconductor–normal metal interface.

Magnetic flux quantization in superconductors allows the implementation of fast and energy-efficient digital superconducting circuits. However, the information representation in magnetic flux severely limits their functional density presenting a long-standing problem. Here we introduce a concept of superconducting digital circuits that do not utilize magnetic flux and have no inductors. We argue that neither the use of geometrical nor kinetic inductance is promising for the deep scaling of superconducting circuits. The key idea of our approach is the utilization of bistable Josephson junctions allowing the representation of information in their Josephson energy. Since the proposed circuits are composed of Josephson junctions only, they can be called all-Josephson junction (all-JJ) circuits. We present a methodology for the design of the circuits consisting of conventional and bistable junctions. We analyze the principles of the circuit functioning, ranging from simple logic cells and ending with an 8-bit parallel adder. The utilization of bistable junctions in the all-JJ circuits is promising in the aspects of simplification of schematics and the decrease of the JJ count leading to space-efficiency.

This paper describes current transport through а long Josephson junction with an alternating critical–current density. This alternating density can be achieved in experiments bу incorporating a magnetic layer to the weak link in а special manner. The prospects for the practical use of such structures are related to the possibility of obtaining bistable Josephson elements on their basis. Joint analysis of both current–phase relations and dynamic characteristics made it possible to optimize the operation mode for a fast superconducting memory cell based on bistable contact and to assess the energy dissipation for the read and write operations.

We consider the current-phase relation (CPR) in the Josephson junctions with complex insulator-superconductor-ferromagnetic interlayers in the vicinity of 0-$\pi$ transition. We find a strong impact of the second harmonic on CPR of the junctions. It is shown that the critical current can be kept constant in the region of 0-pi transition, while the CPR transforms through multi-valued hysteretic states depending on the relative values of tunnel transparency and magnetic thickness. Moreover, CPR in the transition region has multiple branches with distinct ground states., Comment: Submitted in Phys. Rev. B

The results of the study of the impact of single-quantum magnetic flux pulses moving along the Josephson transmission lines (JTL) on the dynamics of states of qubits magnetically coupled with such lines are presented. The JTL dynamics was calculated in the frame of resistively shunted junction model with different damping coefficients. This allowed us to find the form of control current pulses (fluxon) acting on a superconducting qubit. Numerical simulations of the simplest logic operations with superconducting qubit due to calculated fluxon impact are presented.

A superconducting quantum interference device with differential output or "DSQUID" was proposed earlier for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that Spur-Free Dynamic Range (SFDR) of DSQUID magnetic flux-to-voltage transfer function is higher than SFDR > 100 dB while Total Harmonic Distortion (THD) of a signal is less than THD < $10^{-3}\%$ with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, $2��_a = ��_0/8$. Analysis of DSQUID voltage response stability to a variation of the circuit parameters shows that DSQUID implementation allows doing highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply., 7 pages, 5 figures