Quantum tunneling of a single semifluxon in a 0-pi Josephson junction

We consider a symmetric 0-pi Josephson junction of length $L$, which classically can be in one of two degenerate ground states up or down, corresponding to supercurrents circulating clockwise or counterclockwise around the 0-pi boundary. When the length $L$ of the junction becomes smaller than the Josephson penetration depth ${\lambda }_J$, 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 periodic double well potential and estimate parameters for which macroscopic quantum coherence may be observed. We conclude that this system is not very promising to build a qubit because (a) it requires very low temperatures to reach the quantum regime, (b) its tiny flux is hard to read out and © it is very sensitive to the asymmetries between the 0 and pi parts of the junction.