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Fractional Josephson effect is a unique character of Majorana Fermions intopological superconductor system. This effect is very difficult to detectexperimentally because of the disturbance of quasiparticle poisoning andunwanted couplings in the superconductor. Here, we propose a scheme to probefractional DC Josephson effect of semiconductor nanowire-based topologicalJosephson junction through 4{\pi} phase slip. By exploiting a topological RFSQUID system we find that the dominant contribution for Josephson couplingcomes from the interaction of Majorana Fermions, resulting the resonanttunneling with 4{\pi} phase slip. Our calculations with experimentallyreachable parameters show that the time scale for detecting the phase slip istwo orders of magnitude shorter than the poisoning time of nonequilibriumquasiparticles. Additionally, with a reasonable nanowire length the 4{\pi}phase slip could overwhelm the topological trivial 2{\pi} phase slip. Our workis meaningful for exploring the effect of modest quantum fluctuations of thephase of the superconductor on the topological system, and provide a new methodfor quantum information processing.

Detecting fractional Josephson effect through $4\pi$ phase slip