Post-processing of real-time quantum event measurements for an optimal bandwidth.

Single electron tunneling and its transport statistics have been studied for some time using high precision charge detectors. However, this type of detection requires advanced lithography, optimized material systems and low temperatures (mK). A promising alternative, recently demonstrated, is to exploit an optical transition that is turned on or off when a tunnel event occurs. High bandwidths should be achievable with this approach, although this has not been adequately investigated so far. We have studied low temperature resonance fluorescence from a self-assembled quantum dot embedded in a diode structure. We detect single photons from the dot in real time and evaluate the recorded data only after the experiment, using post-processing to obtain the random telegraph signal of the electron transport. This is a significant difference from commonly used charge detectors and allows us to determine the optimal time resolution for analyzing our data. We show how this post-processing affects both the determination of tunneling rates using waiting-time distributions and statistical analysis using full-counting statistics. We also demonstrate, as an example, that we can analyze our data with bandwidths as high as 175 kHz. Using a simple model, we discuss the limiting factors for achieving the optimal bandwidth and propose how a time resolution of more than 1 MHz could be achieved.

Pushing the Limits in Real-Time Measurements of Quantum Dynamics.

Time-resolved studies of quantum systems are the key to understanding quantum dynamics at its core. The real-time measurement of individual quantum numbers as they switch between certain discrete values, well known as a "random telegraph signal," is expected to yield maximal physical insight. However, the signal suffers from both systematic errors, such as a limited time resolution and noise from the measurement apparatus, as well as statistical errors due to a limited amount of data. Here we demonstrate that an evaluation scheme based on factorial cumulants can reduce the influence of such errors by orders of magnitude. The error resilience is supported by a general theory for the detection errors as well as experimental data of single-electron tunneling through a self-assembled quantum dot. Thus, factorial cumulants push the limits in the analysis of random telegraph data, which represent a wide class of experiments in physics, chemistry, engineering, and life sciences.

Shell Filling and Trigonal Warping in Graphene Quantum Dots.

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight, and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold "minivalley degeneracy" caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional s shell and then a p shell are successively filled with four and eight electrons, respectively. For electron numbers larger than 12, as the dot size and the displacement field increase, the single-particle ground state evolves into a threefold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in the magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.

Excited States in Bilayer Graphene Quantum Dots.

We report ground- and excited-state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different from quantum dots in carbon nanotubes, where the two-particle ground state is a spin-singlet state. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35 meV and measure a valley and spin g factor of 36 and 2, respectively.

Optical Detection of Single-Electron Tunneling into a Semiconductor Quantum Dot.

The maximum information of a dynamic quantum system is given by real-time detection of every quantum event, where the ultimate challenge is a stable, sensitive detector with high bandwidth. All physical information can then be drawn from a statistical analysis of the time traces. We demonstrate here an optical detection scheme based on the time-resolved resonance fluorescence on a single quantum dot. Single-electron resolution with high signal-to-noise ratio (4σ confidence) and high bandwidth of 10 kHz make it possible to record the individual quantum events of the transport dynamics. Full counting statistics with factorial cumulants gives access to the nonequilibrium dynamics of spin relaxation of a singly charged dot (γ_{↑↓}=3 ms^{-1}), even in an equilibrium transport measurement.

Optical Blocking of Electron Tunneling into a Single Self-Assembled Quantum Dot.

Time-resolved resonance fluorescence (RF) is used to analyze electron tunneling between a single self-assembled quantum dot (QD) and an electron reservoir. In equilibrium, the RF intensity reflects the average electron occupation of the QD and exhibits a gate voltage dependence that is given by the Fermi distribution in the reservoir. In the time-resolved signal, however, we find that the relaxation rate for electron tunneling is, surprisingly, independent of the occupation in the charge reservoir-in contrast to results from all-electrical transport measurements. Using a master equation approach, which includes both the electron tunneling and the optical excitation or recombination, we are able to explain the experimental data by optical blocking, which also reduces the electron tunneling rate when the QD is occupied by an exciton.