Phase measurements in Aharonov-Bohm interferometers

Details Phase measurements in Aharonov-Bohm interferometers Phase measurements in Aharonov-Bohm interferometers

2003-08-20

arxiv.org/abs/cond-mat/0308414v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

14 pages, lectures at Summer School on Quantum Computation on the Atomic Scale, Istanbul, June 2003. to appear in the Turkish

Scientific paper

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 ${\cal G}$ through the ABI is an even function of the magnetic flux $\Phi=\hbar c\phi/e$ threading the ABI ring. Therefore, if one fits ${\cal G}$ 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 ${\cal G}$ in the closed ABI can be used to extract {\it 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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