Full counting statistics for charge inside a quantum dot

Measurements of the average current and its fluctuation (noise) have been powerful tools to study the quantum transport in mesoscopic systems. Recently it became possible to measure the higher moment of the current probability distribution and moreover, the current distribution itself (‘full counting statistics’ (FCS)) by using quantum point-contact charge-detectors. Motivated by recent experiments, we evaluate the FCS for the probability distribution of electron number inside a quantum dot (QD). We show that a non-Gaussian exponential distribution appears when there is no dot state close to the lead chemical potentials. We propose the measurement of the joint probability distribution of current through the QD and electron number inside the QD, which reveals correlations between the two observables and reflects the asymmetry of tunnel barriers. We also show that for increasing strength of tunneling, the quantum fluctuations qualitatively change the probability distribution of the electron number.