Quantum decoherence in a supersymmetric mechanical system

We make a novel observation about the decoherence phenomenon of the fermion in the Witten's supersymmetric (SUSY) quantum mechanical model. It is shown that, when the bosonic partner in the SUNY model is unobservable in a certain energy scale, the quantum coherence meant by the superposition of fermion states can not be preserved for a long time due to the quantum decoherence induced by the overlooked boson. This refers to a supercharge superselection rule similar to the charge superselection. We numerically calculate the decoherence factor characterizing the extent of decoherence . The obtained result shows the periodic decoherence with finite quantum jump. Some analytic results under the harmonic approximation for the superpotential can be obtained to confirm the numerical calculations.