The Aharanov-Bohm (AB) effect, which predicts that a magnetic field strongly influences the wave function of an electrically charged particle, is investigated in a three site system in terms of the quantum control by an additional dephasing source. The AB effect leads to a non-monotonic dependence of the steady-state current on the gauge phase associated with the molecular ring. This dependence is sensitive to site energy, temperature, and dephasing, and can be explained using the concept of the dark state. Although the phase effect vanishes in the steady-state current for strong dephasing, the phase dependence remains visible in an associated waiting-time distribution, especially at short times. Interestingly, the phase rigidity (i.e., the symmetry of the AB phase) observed in the steady-state current is now broken in the waiting-time statistics, which can be explained by the interference between transfer pathways.
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