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 the 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.
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