We report non-invasive single-charge detection of the full probability distribution Pn of the initialization of a quantum dot with n electrons for rapid decoupling from an electron reservoir. We analyze the data in the context of a model for sequential tunneling pinch-off, which has generic solutions corresponding to two opposing mechanisms. One limit considers sequential "freeze out" of an adiabatically evolving grand canonical distribution, the other one is an athermal limit equivalent to the solution of a generalized decay cascade model. We identify the athermal capturing mechanism in our sample, testifying to the high precision of our combined theoretical and experimental methods. The distinction between the capturing mechanisms allows to derive efficient experimental strategies for improving the initialization. PACS numbers:The fast formation of quantum dots (QDs) out of a two-dimensional electron system (2DES) constitutes an open problem within the field of nanoscale electronics [1]. The initialization process in these dynamic QDs is a key ingredient in, e.g., devices for quantum information processing [2,3], single-electron current sources [4-6], or nanoelectronic circuits [7,8]. The outcome of the initialization is characterized by a probability distribution P n for trapping exactly n electrons in the QD. The goal is to attain a predictable low dispersion distribution thus making dynamic QDs reliable and reproducible sources of electrons on demand. Deviations from this ideal case may be caused, for instance, by backtunneling [9][10][11] or non-adiabatic excitations [12][13][14].

The future redefinition of the international system of units in terms of natural constants requires a robust, high-precision quantum standard for the electrical base unit ampere. However, the reliability of any single-electron current sources generating a nominally quantized output current I = ef by delivering single electrons with charge e at a frequency f is eventually limited by the stochastic nature of the underlying quantum mechanical tunnelling process. We experimentally explore a path to overcome this fundamental limitation by serially connecting clocked single-electron emitters with multiple insitu single-electron detectors. Correlation analysis of the detector signatures during current generation reveals erroneous pumping events and enables us to determine the deviation of the output current from the nominal quantized value ef . This demonstrates the concept of a self-referenced single-electron source for electrical quantum metrology. 1 arXiv:1312.5669v1 [cond-mat.mes-hall]

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Electron counting experiments attempt to provide a current of a known number of electrons per unit time. We propose architectures utilizing a few readily available electron-pumps or turnstiles with modest error rates of 1 part per 10 4 with common sensitive electrometers to achieve the desirable accuracy of 1 part in 10 8 . This is achieved not by counting all transferred electrons but by counting only the errors of individual devices; these are less frequent and therefore readily recognized and accounted for. Our proposal thereby eases the route towards quantum based standards for current and capacitance.