Josephson Junction with a Magnetic-Field Tunable Ground State

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 c so that the effective current-phase relation of this system includes a negative second harmonic proportional to sin(2 psi). If its amplitude is large enough, the ground state of the junction is doubly degenerate psi = +/-phi, where phi 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 proportional to H cos psi in the effective current-phase relation. This results in a nontrivial ground state tunable by magnetic field. The dependence of the critical current on H allows for revealing the ground state experimentally.