Turkish Journal of Physics




In this paper we address measurements of the resonant quantum transmission amplitude t_{QD} = -i t_{QD} e^{i\alpha_{QD}} through a quantum dot (QD), as function of the plunger gate voltage V. Mesoscopic solid state Aharonov-Bohm interferometers (ABI) have been used to measure the ``intrinsic" phase, \alpha_{QD}, when the QD is placed on one of the paths. In a ``closed" interferometer, connected to two terminals, the electron current is conserved, and Onsager's relations require that the conductance G through the ABI is an even function of the magnetic flux \Phi = \hbar c\phi/e threading the ABI ring. Therefore, if one fits G to A+B \cos(\phi+\beta) then \beta only ``jumps" between 0 and \pi, with no relation to \alpha_{QD}. Additional terminals open the ABI, break the Onsager relations and yield a non-trivial variation of \beta with V. After reviewing these topics, we use theoretical models to derive three results on this problem: (i) For the one-dimensional leads, the relation t_{QD} ^2 \propto \sin^2(\alpha_{QD}) allows a direct measurement of \alpha_{QD}. (ii) In many cases, the measured G in the closed ABI can be used to extract both t_{QD} and \alpha_{QD}. (iii) For open ABI's, \beta depends on the details of the opening. We present quantitative criteria (which can be tested experimentally) for \beta to be equal to the desired \alpha_{QD}: the ``lossy" channels near the QD should have both a small transmission and a small reflection.

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