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The visibility of the interference signal in Aharonov-Bohm (AB) interferometers provides information about the coherence of transport channels. For instance, spin-flip processes in interacting quantum dots lead to partial destruction of the coherence [1] and thus reduction of the AB-oscillation amplitude. The occurrence of this effect depends on the dot occupation.
We perform a a weak-coupling perturbation expansion of the Cumulant Generating Function [2] of an AB-Interferometer with quantum dots. Different statistics are found for vanishing and infinite charging energy. Without interaction the interfering part of the statistics is Poisson-like and all moments are even in the AB-flux. Theses statistics are appropriately described also by the Levitov-Formula. In the case of strong Coulomb interaction on the dot, a description in terms of the Levitov-Formula with an effective energy-dependent transmission is still possible for the non-interfering part of the transmission": the non-interacting statistics reappear with a correction due to partial coherence. However, in the presence of both interaction and interference such an effective transmission can only be found for the linear conductance, while the higher moments are inaccessible by a scattering approach. These parts of the statistics show super-poissonian noise and an odd flux dependence. [1] J. König and Y. Gefen, PRL series 86, 3855 (2001). [2] A. Braggio, J. König, and R. Fazio, PRL series 96, 026805 (2006). |
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