We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase psi=pm{phi}. The value of {phi} can be chosen by design in the interval 0<{phi}<pi. The junctions used in our experiments are fabricated as 0-{pi} Josephson junctions of moderate normalized length with asymmetric 0 and {pi} regions. We show that (a) these {phi} Josephson junctions have two critical currents, corresponding to the escape of the phase {psi} from -{phi} and +{phi} states; (b) the phase {psi} can be set to a particular state by tuning an external magnetic field or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.
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