Semifluxons in Superconductivity and Cold Atomic Gases

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 also 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.Comment: 15 pages (Latex), 6 color figures (eps

Quantum tunneling of semifluxons

We consider a system of two semifluxons of opposite polarity in a 0-pi-0 long Josephson junction, which classically can be in one of two degenerate states: up-down or down-up. When the distance $a$ between the 0-pi boundaries (semifluxon's centers) is a bit larger than the crossover distance $a_c$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling. We map this problem to the dynamics of a single particle in a double well potential and estimate parameters for which quantum effects emerge. We also determine the classical-to-quantum crossover temperature as well as the tunneling rate (energy level splitting) between the states up-down and down-up.Comment: submitted to PRB, comments/questions are welcom