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We investigate theoretically the noise and the full counting statistics of electrons that are emitted from a superconductor into two spatially separated quantum dots by the splitting of Cooper pairs and further on collected in two normal-state electrodes. With negatively-biased drain electrodes and a large superconducting gap, the dynamics of the Cooper pair splitter can be described by a Markovian quantum master equation. Using techniques from full counting statistics, we evaluate the electrical currents, their noise power spectra, and the power-power correlations in the output leads. The current fluctuations can be attributed to the competition between Cooper pair splitting and elastic cotunneling between the quantum dots via the superconductor. In one regime, these processes can be clearly distinguished in the cross-correlation spectrum with peaks and dips appearing at characteristic frequencies associated with elastic cotunneling and Cooper pair splitting, respectively. We corroborate this interpretation by analyzing the charge transport fluctuations in the time domain, specifically by investigating the $g^{(2)}$-function of the output currents. Our work identifies several experimental signatures of the fundamental transport processes involved in Cooper pair splitting and provides specific means to quantify their relative strengths. As such, our results may help guide and interpret future experiments on current fluctuations in Cooper pair splitters., Comment: 15 pages, 6 figures

By means of an electron hole rate equation model we explain the phase dynamics of a quantum dot semiconductor optical amplifier and the appearance of different decay times observed in pump and probe experiments. The ultrafast hole relaxation leads to a first ultrafast recovery of the gain, followed by electron relaxation and, in the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. We explain the ultrafast response of quantum dot amplifiers as an effect of hole escape and recombination without the need to assume Auger processes.

We propose a scheme of rate equations for stable dimers that permits the description quite satisfactorily of the evolution of the number of islands in the entire range of surface coverage. The characteristic time for coalescence and the capture number are computed through a stochastic approach for both random and nonrandom arrangements of nuclei. Rate equations are applied to describe kinetic Monte Carlo simulations previously published, in the whole range of surface coverages. It is found that to reproduce the simulation, the effect of the nonrandomicity of the nuclei distribution must be taken into account.

Multiphoton ionisation and dissociation of NO2 has been studied experimentally at 375 nm for laser pulse widths of 10 ns and 50 fs. The parent NO2 ion peak is not seen in the ns data. In all spectra, the main peak observed is due to the ionisation of the NO molecule which results from the dissociation of excited NO2 formed after absorbing a 375 nm photon. The intensity dependencies of both NO and NO2 ion peaks have also been measured. The data has been analysed within the context of a rate equation model using published cross-sections and dissociation rates except for the two-photon ionisation cross-section for NO2 which was chosen to reproduce the NO2/NO ion signal ratios at 50 fs. The rate equation model provides a good description of the complete set of data. Indirectly, it may be concluded that coherence effects do not play an important role in the multiphoton excitation/ionisation of NO2. The data also rules out the importance of above-ionisation dissociation in NO2 - a conclusion which is consistent with previous data at 496 and 248 nm for laser pulse widths greater than or equal to 300 fs. Chemical Physics Letters

The exceptional performance of self-assembled Quantum Dot (QD) materials renders them extremely appealing for their use as optical communications devices. As lasers, they feature reduced and temperature independent threshold current and proper emission wavelength at the fiber telecommunication windows. These characteristics, together with the low linewidth enhancement factor and broad spectrum, make QD materials extremely attractive for application as light emitters or amplifiers. There exist, nevertheless, several unclear issues which prevent QDs from conquering the new generation of optoelectronic devices. Their differential efficiency is lower than expected. The output power of QD lasers is lower than that of their quantum well counterpart. Still, it is their dynamics which has incited the majority of studies. The modulation bandwidth of these devices seems to be limited by the relaxation of carriers from the upper energetic layers to the low levels within the dot. Besides, the electron-hole interaction is widely unknown, the extent of the electron-hole Coulombic attraction is not yet established. Throughout this thesis I present a theoretical and experimental study of the gain and phase dynamics of quantum dot lasers. I explain the appearance of different decay times observed in pump and probe experiments in QD amplifiers as a result of the different electron and hole relaxation times, by means of an electron-hole rate-equation model. The ultrafast hole relaxation first leads to an ultrafast recovery of the gain, which is then followed by electron relaxation and, on the nanosecond timescale, radiative and non-radiative recombinations. The phase dynamics is slower and is affected by thermal redistribution of carriers within the dot. Our results corroborate with spectral measurements of the dephasing and gain in QD amplifiers. Additionally, our work is compared with existing pump and probe results. Exploiting the capacity of QD lasers to emit at two different wavelengths corresponding to the ground state (GS) and excited state (ES), I present a theoretical study of the QD dynamics, based on a linearization of the QD rate-equations. The results predict the existence of single oscillation frequency of GS and ES, meaning that both states are highly coupled. In order to verify our theory, we perform two kinds of experiments. By modulating these lasers at high frequency, we measure separately the dynamics of GS and ES. However, in contradiction to our theory, two different modulation frequencies are found. Additional temporally-resolved measurements of the laser dynamics reveal a surprising effect. By injecting a sub-bandgap pump in an InAs/InGaAs QD laser, the emitted photons are depleted. Through additional transmission and photocurrent measurements, we relate this observation with carrier photoexcitation, which was so far only theoretically addressed. The role of carrier photoexcitation in our experimental laser dynamics is further supported by a rate-equation model. Impelled by this finding, we study the effect of carrier photoexcitation in the static and dynamic characteristics. We find that carrier photoexcitation reduces the efficiency of QD lasers, which is one of the major QD handicaps, and depletes the GS lasing after the ES threshold, as observed experimentally. Moreover, by adding carrier photoexcitation to our linearization of the rate-equations, we find that the theory predicts the appearance of two lasing resonance frequencies, in agreement with our previous experimental results. Additionally, we deal with the improvement of carrier relaxation. In tunnel injection devices, carriers are given an additional path towards the ground state of the dot by growing a quantum well layer close to the QD active plane. Through the quantum-mechanical tunneling effect, carriers relax from the nearby quantum well layer to the QDs, which speeds up relaxation. We aim at the increase of the modulation bandwidth while keeping the good performances quantum dot lasers have exhibited, such as low and temperature insensitive threshold current and proper emission wavelength. In the final part of this work, we present dynamical measurements of 1.5 µm InAs/InP tunnel injection and non-tunnel injection QD lasers, which display remarkable static characteristics. After proving with static measurements that tunnel injection is actually taking place in these structures, we show several dynamic measurements. Pump and probe measurements on QD devices show that the tunnel injection samples exhibit a slightly faster relaxation time than the non-tunnel injection samples used as reference, meaning that relaxation time is improved with tunnel injection. However, by probing the device with an ultrafast pump no improvement of the dynamic characteristics is observed. These results confirm that the laser dynamic properties of InP QD lasers, both standard and tunnel-injection designs, are actually not limited by relaxation of carriers. We point towards the size distribution of these quantum dash-like structures as the limiting factor of the modulation frequency.