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We show how the superconducting phase difference in a Josephson junction maybe used to split the Kramers degeneracy of its energy levels and to remove allthe properties associated with time reversal symmetry. The superconductingphase difference is known to be ineffective in two-terminal short Josephsonjunctions, where irrespective of the junction structure the induced Kramersdegeneracy splitting is suppressed and the ground state fermion parity muststay even, so that a protected zero-energy Andreev level crossing may neverappear. Our main result is that these limitations can be completely avoided byusing multi-terminal Josephson junctions. There the Kramers degeneracy breakingbecomes comparable to the superconducting gap, and applying phase differencesmay cause the change of the ground state fermion parity from even to odd. Weprove that the necessary condition for the appearance of a fermion parityswitch is the presence of a "discrete vortex" in the junction: the situationwhen the phases of the superconducting leads wind by $2\pi$. Our approachoffers new strategies for creation of Majorana bound states as well as spinmanipulation. Our proposal can be implemented using any low density, highspin-orbit material such as InAs quantum wells, and can be detected usingstandard tools.

Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions