Analysis of the phase lapse problem in closed interferometers

We investigate the connection between the asymmetry of the Fano resonances in a mesoscopic interferometer with an embedded quantum dot and the pi lapses in the phase of the "bare" dot transmittance. Consecutive Fano resonances with the same (opposite) sign of the Fano parameter imply the presence (absence) of a phase lapse with pi between the corresponding resonances of the dot. Our results suggest that the famous "phase lapse" problem, first reported by Schuster et al. [R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H. Shtrikman, Nature 385 (1997) 417], can therefore be experimentally addressed in closed interferometers. It is also proposed that the Fano effect can be used to extract the phase distributions of the eigenfunctions for a mesoscopic 20 shape, via the parity of the resonances. In the presence of electron-electron interaction, one can calculate the phases of the T-matrix elements. The numerical results lead to the same conclusions as for the non-interacting case. (C) 2012 Elsevier B.V. All rights reserved.