Traveling electromagnetic waves in annular Josephson tunnel junctions

Abstract

It is well known that long Josephson tunnel junctions (JTJs) act as active transmission lines for the slow-mode propagation of magnetic flux-quanta (in the form of solitary waves) that is at the base of many superconducting circuits. At the same time, they support the propagation of quasi-TEM dispersive waves with which the magnetic flux non-linearly interact. In this work, we study the properties of the electromagnetic resonances, under different conditions of practical interest, in annular JTJs (AJTJs), in which the wavelengths are limited to the length of the circumference divided by an integer. Our analysis is based on perturbed sine-Gordon equations the (1+1)-dimensional space with periodic boundary conditions. We discuss the discrete modes of the travelling EM waves in circular annular JTJs in the presence of an in-plane magnetic field, as well as in the recently introduced confocal annular JTJs (in the absence of magnetic field). In both cases, a variable-separation method leads to quantitatively different Mathieu equations characterized by even and odd spatially periodic solutions with different eigenfrequencies. It implicates that a single mode circulating wave is given by the superposition of two standing waves with the same wavelengths but different frequencies, and so has a periodically inverting direction of propagation. The control parameters of this frequency splitting are the in-plane magnetic field amplitude for the circular AJTJ and the aspect ratio for the confocal AJTJs. In the appropriate limits, the previously known solutions Email address: r.monaco@isasi.cnr.it and roberto.monaco@cnr.it (Roberto Monaco)

Field cooled annular Josephson tunnel junctions

“…There is a continuously growing interest for novel applications and multi-fluxon dynamic states in annular Josephson systems [1][2][3] boundaries of the annular tunnel barrier are closely spaced confocal ellipses 5,6 , rather than concentric circles as for in the classical circular AJTJs. The physics of Josephson tunnel junctions is known to drastically depend on their geometrical configurations 7 ; indeed, the phenomenology of a confocal AJTJ is strongly affected by its aspect ratio, ρ, defined as the ratio of the mean length of the minor axes to the mean length of the major axes of the annulus 8 .…”

“…There is a continuously growing interest for novel applications and multi-fluxon dynamic states in annular Josephson systems [1][2][3]. Recently [4], the unidirectional collective motion of a dense train of fluxons in Josephson junctions, called Josephson flux-flow, has been first reported in current-biased planar Annular Josephson Tunnel Junctions (AJTJs) under the application of an in-plane uniform magnetic field generating fluxflow steps (FFSs) in their current-voltage characteristics.…”

Flux-flow effects in annular Josephson tunnel junctions

“…The interaction between the fluxon and the small amplitude waves destabilizes its forward advancement and prevents it from reaching relativistic speeds 25 . The dispersion relation of plasma waves in confocal AJTJs has been recently investigated in the absence of trapped fluxons 51 . It was found that for each discrete mode m, that corresponds to a wavelength equal to the annulus circumference divided by m, two eigenfrequencies exist that are related to the even and odd spatial dependence of the wave.…”

ac-locking of thermally-induced sine-Gordon breathers

“…Due to its nontopological structure, mastering the breather's physics is a very tough challenge. In particular, experimental evidence of this oscillating state has yet to be provided in LJJs, despite the numerous investigations on the matter [17][18][19][20][21][22][23], primarily due to its friction-triggered radiative decay and its elusiveness with respect to I -V measurements [20,24]. The Josephson breather's detection would, therefore, solve a long-lasting problem in nonlinear science, but it would also pave the way for several applications in, e.g., information transmission [25], quantum computation [26], generation of THz radiation [27].…”