Conditional counting statistics of electrons tunneling through quantum dot systems measured by a quantum point contact

TL;DR

This paper develops a new, efficient method for calculating the conditional counting statistics of electron transport in quantum dot systems monitored by a quantum point contact, revealing detailed insights into transport properties and shot noise effects.

Contribution

The authors introduce a novel, numerically stable method for conditional counting statistics applicable to complex quantum dot systems, surpassing existing techniques in stability and parameter range.

Findings

Conditional current cumulants differ significantly from unconditional ones.

QPC shot noise influences the conditional counting statistics.

Discrepancies observed between sequential and coherent tunneling models.

Abstract

We theoretically study the conditional counting statistics of electron transport through a system consisting of a single quantum dot (SQD) or coherently coupled double quantum dots (DQD's) monitored by a nearby quantum point contact (QPC) using the generating functional approach with the maximum eigenvalue of the evolution equation matrix method, the quantum trajectory theory method (Monte Carlo method), and an efficient method we develop. The conditional current cumulants that are significantly different from their unconditional counterparts can provide additional information and insight into the electron transport properties of mesoscopic nanostructure systems. The efficient method we develop for calculating the conditional counting statistics is numerically stable, and is capable of calculating the conditional counting statistics for a more complex system than the maximum eigenvalue method and for a wider range of parameters than the quantum trajectory method. We apply our method to investigate how the QPC shot noise affects the conditional counting statistics of the SQD system, going beyond the treatment and parameter regime studied in the literature. We also investigate the case when the interdot coherent coupling is comparable to the dephasing rate caused by the back action of the QPC in the DQD system, in which there is considerable discrepancy in the calculated conditional current cumulants between the population rate (master-) equation approach of sequential tunneling and the full quantum master-equation approach of coherent tunneling.