Conditional counting statistics of electrons tunneling through quantum dot system measured by a quantum point contact
Yen Jui,Chang1*, Hsi-Sheng Goan1
1Department of Physics, National Taiwan University, Taipei, Taiwan
* presenting author:Yen Jui Chang,
The conditional counting statistics (CCS) that is the statistical current fluctuations of one system given the observation of a particular current in the other system can be substantially different from their unconditional counterparts. We provide a numerical method useful to calculate the CCS of nanostructure transport systems when the eigenvalues of the counting field matrix in the number-resolved master equation approach are not analytically available. We apply our method to study the CCS of a system consisting of a single quantum dot (SQD) or double quantum dots (DQD’s) coupled in series, monitored by a quantum point contact (QPC) nearby. The CCS results for simple SQD-QPC system obtained by our method recover those by different methods in various limiting cases in the literature. We then apply our method to the more complex DQD-QPC system where the CCS is difficult to calculate by other method. The CCS can provide more information and insight to the electron transport properties than the unconditional one. We show that the results of the CCS of the DQD-QPC system in the high and low inter-dot coupling regimes can be inferred from those of the SQD-QPC system through the concept of effective tunneling rates.

Keywords: counting statistics