Dephasing and Measurement Efficiency via a Quantum Dot Detector

TL;DR

This paper investigates how a quantum dot detector influences charge detection and dephasing in a mesoscopic system, revealing unique resonance behaviors and the role of scattering matrix properties in measurement efficiency.

Contribution

It demonstrates the relationship between dephasing rate and conductance in a resonant quantum dot detector, highlighting unusual resonance effects on measurement efficiency.

Findings

Dephasing rate is proportional to the square of the QDD conductance.

Measurement rate dips near the resonance of the QDD.

Detector efficiency vanishes at resonance in symmetric, resonant detectors.

Abstract

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.