Counting Statistics for Electron Capture in a Dynamic Quantum Dot

Abstract

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].

High-resolution error detection in the capture process of a single-electron pump

“…9,11 The decay cascade model yielded a better fit, as was also found at the much lower temperature of 25 mK. 9 The plateaus are considerably sharper using the slow loading pulse, consistent with pumped current measurements in which the rise time (proportional to the inverse of the pumping frequency) was varied in the 1 À 10 ns range. 5 Our technique allows the investigation of rise times over many orders of magnitude, including those too slow to generate a measurable pumped current.…”

“…As expected from DC measurements with the pump in a magnetic field, 5,7,8,20 there are a series of wide plateaus where one value of N dominates the loading statistics. This is highlighted by color-coding data points black when all the cycles yielded the same value of N. Comparable data have been presented previously, 9 but at zero magnetic field where the regime of very accurate loading could not be accessed. We calculated hNi ¼ P NP N for the fast loading data, and fitted it to both the decay cascade model 4,15 (Fig.…”

“…Recently, DC measurements 8 have shown that $6 Â 10 8 electrons per second can be transferred through a QD with an average error rate as low as 2 Â 10 À7 . To probe the individual probabilities P n , mesoscopic charge detectors need to be used to measure the number of electrons pumped onto charge sensing islands, [9][10][11][12] with the lowest reported error probability, 10 À4 , achieved in a silicon QD pump.…”

“…We use a quantum point contact (QPC) charge detector strongly coupled to the QD to probe the number of loaded electrons. The use of a QPC instead of a SET detector 9,10 allows operation in strong magnetic fields. Electrons can be loaded with fast voltage waveforms, as used in high-speed pumping experiments 5,8 and then probed on millisecond time-scales required for high-fidelity readout.…”

Noise of a single-electron emitter

“…29 Indeed, the measurements 30 show a significant reduction of the lowfrequency noise power in the quantized emission regime, when the source emits the same number of electrons, in particular one electron, during each working period. The direct counting of the number of particles emitted in each cycle was demonstrated by measuring the partition noise of the beam-splitter 31 and with the help of a charge detector 32 .…”