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We elaborate a theoretical description of large Josephson junctions which is based on the Werthamers microscopic tunneling theory. The model naturally incorporates coupling of electromagnetic radiation to the tunnel currents and, therefore, is particularly suitable for description of the self-coupling effect in Josephson junction. In our numerical calculations we treat the arising integro-differential equation, which describes temporal evolution of the superconducting phase difference coupled to the electromagnetic field, by the Odintsov-Semenov-Zorin algorithm. This allows us to avoid evaluation of the time integrals at each time step while taking into account all the memory effects. To validate the obtained microscopic model of large Josephson junction we focus our attention on the Josephson flux flow oscillator. The proposed microscopic model of flux flow oscillator does not involve the phenomenological damping parameter, rather, the damping is taken into account naturally in the tunnel current amplitudes calculated at a given temperature. The theoretically calculated current-voltage characteristics is compared to our experimental results obtained for a set of fabricated flux flow oscillators of different lengths. Our theoretical calculation agrees well with the obtained experimental results, and, to our knowledge, is the first where theoretical description of Josephson flux flow oscillator is brought beyond the perturbed sine-Gordon equation.
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Since the very first experimental realization of Josephson flux-flow oscillator (FFO), its theoretical description has been limited by the phenomenological per- turbed sine-Gordon equation (PSGE). While PSGE can qualitatively describe the topological excitations in Josephson junctions that are sine-Gordon solitons or flux- ons, it is unable to capture essential physical phenomena of a realistic system such as the coupling between tunnel currents and electromagnetic radiation. Furthermore, PSGE neglects any dependence on energy gaps of superconductors and makes no distinction between symmetric and asymmetric junctions: those made of two iden- tical or two different superconducting materials. It was not until recently when it became possible to calculate properties of FFO by taking into account information about energy gaps of superconductors [D. R. Gulevich et al., Phys. Rev. B 96, 024215 (2017)]. Such approach is based on the microscopic tunneling theory and has been shown to describe essential features of symmetric Nb-AlOx-Nb junctions. Here we extend this approach to asymmetric Nb-AlN-NbN junctions and compare the calculated current-voltage characteristics to our experimental results.
The current-voltage and spectral characteristics of a flux flow oscillator (FFO), based on a long Josephson junction, are studied. The investigations are performed in the range of small bias currents and magnetic fields, where the FFO radiates a quasi-chaotic signal with extremely large radiation linewidth, and the displaced linear slope (DLS) is observed at the current-voltage characteristic. By direct numerical simulation of the sine-Gordon equation it is demonstrated that for large lengths of the Josephson junction or in the case of finite matching of the FFO with external waveguide system, the DLS with extremely large linewidth is transformed into Fiske steps with very narrow linewidth. While there is the common belief that the chaotic regime of the FFO is due to excitation of the internal oscillation modes in the soft fluxon chain, it is demonstrated that this regime is inspired by multiple reflections of the traveling waves from junction ends.
MiTMoJCo (Microscopic Tunneling Model for Josephson Contacts) is C code which aims to assist modeling of superconducting Josephson contacts based on the microscopic tunneling theory. The code offers implementation of a computationally demanding part of this calculation, that is evaluation of superconducting pair and quasiparticle tunnel currents from the given tunnel current amplitudes (TCAs) which characterize the junction material. MiTMoJCo comes with a library of pre-calculated TCAs for frequently used Nb-AlOx-Nb and Nb-AlN-NbN junctions, a Python module for developing custom TCAs, supplementary optimum filtration module for extraction of a constant component of a sinusoidal signal and examples of modeling few common cases of superconducting Josephson contacts.
For the first time the linewidth of Flux-Flow Oscillator has been calculated by direct computer simulation of the sine-Gordon equation with noise. Nearly perfect agreement of the numerical results with the formula derived in [Phys. Rev. B, {bf 65}, 054504 (2002)] has been achieved. It has been demonstrated that for homogeneous bias current distribution the linewidth actually does not depend on the junction length for practically interesting parameters range. Depending on the length of the unbiased tail, the power may be maximized and the linewidth may be minimized in a broad range of bias currents. The linewidth can be decreased further by 1.5 times by proper load matching.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and wells form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be essentially increased, by engineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset-day technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation between ground and excited states, which consists of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within semiclassical approximation by instanton technique show good correlation with a numerical solution.
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