We consider a short Josephson junction with a phase discontinuity $kappa$ created, e.g., by a pair of tiny current injectors, at some point $x_0$ along the length of the junction. We derive the effective current-phase relation (CPR) for the system as
a whole, i.e., reduce it to an effective point-like junction. From the effective CPR we obtain the ground state of the system and predict the dependence of its critical current on $kappa$. We show that in a large range of $kappa$ values the effective junction behaves as a $varphi_0$ Josephson junction, i.e., has a unique ground state phase $varphi_0$ within each $2pi$ interval. For $kappaapproxpi$ and $x_0$ near the middle of the junction one obtains a $varphi_0pmvarphi$ junction, i.e., the Josephson junction with degenerate ground state phase $varphi_0pmvarphi$ within each $2pi$ interval. Further, in view of possible escape experiments especially in the quantum domain, we investigate the scaling of the energy barrier and eigenfrequency close to the critical currents and predict the behavior of the escape histogram width $sigma(kappa)$ in the regime of the macroscopic quantum tunneling.
We consider a $varphi$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $psi=pmvarphi$. In the non-zero voltage state the phase moves viscously along a tilted periodic double-well potential. When the tilting is r
educed quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($-varphi$ or $+varphi$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to zero-voltage state. In the limit of low damping the $varphi$ Josephson junction exhibits a butterfly effect --- extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.
The $varphi$ Josephson junction has a doubly degenerate ground state with the Josephson phases $pmvarphi$. We demonstrate the use of such a $varphi$ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic fie
ld and reading by applying a bias current. In the store state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with Rapid Single Flux Quantum logic is possible.
We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-pi-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the len
gth of the pi-junction, the detuning of the optical transition, or the strength of the laser-coupling, to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-pi-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase-diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation.
We consider an asymmetric 0-pi Josephson junction consisting of 0 and pi regions of different lengths L_0 and L_pi. As predicted earlier this system can be described by an effective sine-Gordon equation for the spatially averaged phase psi so that th
e effective current-phase relation of this system includes a emph{negative} second harmonic ~sin(2 psi). If its amplitude is large enough, the ground state of the junction is doubly degenerate psi=pmvarphi, where varphi depends on the amplitudes of the first and second harmonics. We study the behavior of such a junction in an applied magnetic field H and demonstrate that H induces an additional term ~H cos(psi) in the effective current-phase relation. This results in a non-trivial ground state emph{tunable} by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.
Josephson junctions and junction arrays are well studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is al
so possible to device two different types of junctions: depending on the sign of the critical current density, they are called 0- or pi-junction. In turn, a 0-pi junction is formed by joining two of such junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0-pi boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0-pi Josephson junction is created by the phase of a complex valued Rabi-frequency and we a derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.
We fabricated high quality Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb superconductor-insulator-ferromagnet-superconductor Josephson tunnel junctions. Using a ferromagnetic layer with a step-like thickness, we obtain a 0-pi junction, with equal lengths and critic
al currents of 0 and pi parts. The ground state of our 330 microns (1.3 lambda_J) long junction corresponds to a spontaneous vortex of supercurrent pinned at the 0-pi step and carrying ~6.7% of the magnetic flux quantum Phi_0. The dependence of the critical current on the applied magnetic field shows a clear minimum in the vicinity of zero field.
We investigate the creation of an arbitrary $kappa$-discontinuity of the Josephson phase in a long Nb-AlO_x-Nb Josephson junction (LJJ) using a pair of tiny current injectors, and study the formation of fractional vortices formed at this discontinuit
y. The current I_inj, flowing from one injector to the other, creates a phase discontinuity kappa ~ I_inj. The calibration of injectors is discussed in detail. The small but finite size of injectors leads to some deviations of the properties of such a 0-kappa-LJJ from the properties of a LJJ with an ideal kappa-discontinuity. These experimentally observed deviations in the dependence of the critical current on I_inj$ and magnetic field can be well reproduced by numerical simulation assuming a finite injector size. The physical origin of these deviations is discussed.
We propose, implement and test experimentally long Josephson 0-pi junctions fabricated using conventional Nb-AlOx-Nb technology. We show that using a pair of current injectors, one can create an arbitrary discontinuity of the Josephson phase and in p
articular a pi-discontinuity, just like in d-wave/s-wave or in d-wave/d-wave junctions, and study fractional Josephson vortices which spontaneously appear. Moreover, using such junctions, we can investigate the emph{dynamics} of the fractional vortices -- a domain which is not yet available for natural 0-pi-junctions due to their inherently high damping. We observe half-integer zero-field steps which appear on the current-voltage characteristics due to hopping of semifluxons.
