Electron counting in quantum dots

We use time-resolved charge detection techniques to investigate single-electron tunneling in semiconductor quantum dots. The ability to detect individual charges in real-time makes it possible to count electrons one-by-one as they pass through the structure. The setup can thus be used as a high-precision current meter for measuring ultra-low currents, with resolution several orders of magnitude better than that of conventional current meters. 
In addition to measuring the average current, the counting procedure also makes it possible to investigate correlations between charge carriers. In quantum dots, we find that the strong Coulomb interaction makes electrons try to avoid each other. This leads to electron anti-bunching, giving stronger correlations and reduced noise compared to a current carried by statistically independent electrons. 
The charge detector is implemented by monitoring changes in conductance in a near-by capacitively coupled quantum point contact. We find that the quantum point contact not only serves as a detector but also causes a back-action onto the measured device. Electron scattering in the quantum point contact leads to emission of microwave radiation. The radiation is found to induce an electronic transition between two quantum dots, similar to the absorption of light in real atoms and molecules. Using a charge detector to probe the electron transitions, we can relate a single-electron tunneling event to the absorption of a single photon. Moreover, since the energy levels of the double quantum dot can be tuned by external gate voltages, we use the device as a frequency-selective single-photon detector operating at microwave energies.

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account. The second law of thermodynamics states that a macroscopic system out of thermal equilibrium will irreversibly move toward equilibrium driven by a steady increase of its entropy. This macroscopic irreversibility occurs despite the time-reversal symmetry of the underlying microscopic equations of motion. Also, a microscopic system will undergo an irreversible evolution on a long time scale, but, over a sufficiently short observation time � , both entropy-producing trajectories as well as their timereversed entropy-consuming counterparts occur. It is only because of the statistics of these occurrences that a longterm irreversible evolution is established. This phenomenon is described by the fluctuation theorem [1,2]. Irrespective of the description of the trajectories being system-specific, the fluctuation theorem (FT) relates the probabilities P� ð� SÞ for processes that change the entropy

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Irreversibility on the Level of Single-Electron Tunneling

We report measurements of the cross correlation between temporal current fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. We find good agreement with the data by including an interdot Coulomb interaction in a sequential-tunneling model.

Tunable noise cross correlations in a double quantum dot.

We present measurements of the fourth and fifth cumulants of the distribution of transmitted charge in a tunable quantum dot. We investigate how the measured statistics is influenced by the finite bandwidth of the detector and by the finite measurement time. By including the detector when modeling the system, we use the theory of full counting statistics to calculate the noise levels for the combined system. The predictions of the finite bandwidth model are in good agreement with measured data.

Measurements of higher-order noise correlations in a quantum dot with a finite bandwidth detector

We present time-resolved measurements of electron transport through a quantum dot. The measurements were performed using a nearby quantum point contact as a charge detector. The rates for tunneling through the two barriers connecting the dot to source and drain contacts could be determined individually. In the high bias regime, the method was used to probe excited states of the dot. Furthermore, we have detected bunching of electrons, leading to super-Poissonian noise. We have used the framework of full counting statistics to model the experimental data. The existence of super-Poissonian noise suggests a long relaxation time for the involved excited state, which could be related to the spin relaxation time.

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Counting statistics and super-Poissonian noise in a quantum dot: Time-resolved measurements of electron transport

We present measurements of the magnetoresistance of a two-dimensional electron gas (2DEG) under continuous microwave as a function of the irradiation frequency. In a previous work by Simovic et al. [Phys. Rev. B 71 (2005) 233303], the magnetoresistance under microwave was shown to be modulated by oscillations of large amplitude that are periodic with magnetic field, their period and phase depending strongly on the electron density. Here we show that the phase and the amplitude of the microwave-induced oscillations also depend on the frequency of irradiation and the sign of the magnetic field.

B. Simovič

Papers

Counting statistics and super-Poissonian noise in a quantum dot: Time-resolved measurements of electron transport

Oscillations of the magnetoresistance of a two-dimensional electron gas under microwave irradiation: Influence of the irradiation frequency