Measuring the Transmission Phase of a Quantum Dot in a Closed Interferometer

The electron transmission through a closed Aharonov-Bohm mesoscopic solid-state interferometer, with a quantum dot (QD) on one of the paths, is calculated exactly for a simple model. Although the conductance is an even function of the magnetic flux (due to Onsager’s relations), in many cases one can use the measured conductance to extract both the amplitude and the phase of the “intrinsic” transmission amplitude $t_D=-i|t_D|e^{i{\alpha }_D}$ through the “bare” QD. We also propose to compare this indirect measurement with the (hitherto untested) direct relation ${sin}^2({\alpha }_D)\equiv |t_D{|}^2/\max (|t_D{|}^2)$.

Figure 1

Model for the closed ABI.

Figure 2

AB transmission $\mathcal{T}$ versus the AB phase $\varphi$ and the gate voltage $V$, for one (left) and two (right) noninteracting resonances.