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 demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase psi=pm{phi}. The value of {phi} can be chosen by design in the interval 0<{phi}<pi. The junctions used in our e
xperiments are fabricated as 0-{pi} Josephson junctions of moderate normalized length with asymmetric 0 and {pi} regions. We show that (a) these {phi} Josephson junctions have two critical currents, corresponding to the escape of the phase {psi} from -{phi} and +{phi} states; (b) the phase {psi} can be set to a particular state by tuning an external magnetic field or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.
In long Josephson junctions with multiple discontinuities of the Josephson phase, fractional vortex molecules are spontaneously formed. At each discontinuity point a fractional Josephson vortex carrying a magnetic flux $|Phi|<Phi_0$, $Phi_0approx 2.0
7times 10^{-15}$ Wb being the magnetic flux quantum, is pinned. Each vortex has an oscillatory eigenmode with a frequency that depends on $Phi/Phi_0$ and lies inside the plasma gap. We experimentally investigate the dependence of the eigenfrequencies of a two-vortex molecule on the distance between the vortices, on their topological charge $wp=2piPhi/Phi_0$ and on the bias current $gamma$ applied to the Josephson junction. We find that with decreasing distance between vortices, a splitting of the eigenfrequencies occurs, that corresponds to the emergence of collective oscillatory modes of both vortices. We use a resonant microwave spectroscopy technique and find good agreement between experimental results and theoretical predictions.
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.
We consider a fractional Josephson vortex in a long 0-kappa Josephson junction. A uniformly applied bias current exerts a Lorentz force on the vortex. If the bias current exceeds the critical current, an integer fluxon is torn off the kappa-vortex an
d the junction switches to the voltage state. In the presence of thermal fluctuations the escape process takes place with finite probability already at subcritical values of the bias current. We experimentally investigate the thermally induced escape of a fractional vortex by high resolution measurements of the critical current as a function of the topological charge kappa of the vortex and compare the results to numerical simulations for finite junction lengths and to theoretical predictions for infinite junction lengths. To study the effect caused by the junction geometry we compare the vortex escape in annular and linear junctions.
