Coherent superpositions of single semifluxon states in a $0\text{−}\pi$ Josephson junction

We consider a symmetric $0\text{−}\pi$ Josephson junction of length $L$, which classically can be in one of two degenerate ground states $\uparrow$ or $\downarrow$, corresponding to supercurrents circulating clockwise or counterclockwise around the $0\text{−}\pi$ 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 to the neighboring well. 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 experimentally. 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 (c) it is very sensitive to the asymmetries between the 0 and $\pi$ parts of the junction.

Figure 1

(Color online) Schematic drawing of a $0\text{−}\pi$ JJ and magnetic field profiles in two degenerate ground states. Gray curves show the magnetic field profile in an infinite JJ (solid line is semifluxon, dashed line is antisemifluxon, $\Phi =\pm {\Phi }_0/2$). Black curves show corresponding solutions in the JJ of finite length. In this case the magnetic flux (the area under the corresponding curve) $\left|\Phi \right|<{\Phi }_0/2$.

Figure 2

(Color online) The two lowest energy levels $E_1$ and $E_2$, $\Delta E=E_2-E_1$, and the barrier height $U_0$ (all given in mK) as a function of $\ell$ for typical parameters given in the text.

Figure 3

(Color online) Solutions of the Schrödinger Eq. (22) for (a) $\ell =0.13$ and (b) $\ell =0.09$.