Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 05/05 Archiv

Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. In this Thesis we address two of the most significant technological challenges towards developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. To this end, we develop novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability. In the first part of this Thesis, we investigate electron transport through single and double QDs, with the aim of harnessing the (dissipative) coupling to the electronic degrees of freedom for the creation of coherence in both the transient and steady-state behaviour of the ambient nuclear spins. First, we theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a single QD. To this end, we first develop a master-equation-based formalism for electron transport in the Coulomb-blockade regime assisted by hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. When starting from an initially uncorrelated, highly polarized state, the nuclear system experiences a strong correlation buildup, due to the collective nature of the coupling to the central electron spin. We demonstrate that this results in a sudden intensity burst in the electronic tunneling current emitted from the QD system, which exceeds the maximal current of a corresponding classical system by several orders of magnitude. This gives rise to the new paradigm of electronic superradiance. Second, building upon the insight that the nuclear spin dynamics are governed by collective interactions giving rise to coherent effects such as superradiance, we propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics is shown to lead to intriguing effects such as multistability and criticality in the steady-state solutions. In the second part of this Thesis, our focus turns towards the realization of long-range spin-spin coupling between remote qubits. We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitations can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits. In summary, this thesis provides contributions towards developing a scalable quantum information processor based on spins in quantum dots in two different aspects. The first part is dedicated to a deeper understanding of the nuclear spin dynamics in quantum dots. In the second part we put forward a novel sound-based strategy to realize long-range spin-spin coupling between remote qubits. This completes a broad picture of spin-based quantum information processing which integrates different perspectives, ranging from the single-qubit level to a broader quantum network level.

Ultrafast electron diffraction is a pump--probe technique that allows the visualisation of molecular dynamics with atomic scale resolution. However, the fastest electronic and atomic dynamics in light-driven matter transformations are, as yet, unmeasureable with this technique. This is because the temporal resolution in ultrafast electron diffraction is limited by difficulties in producing the shortest electron pulses, caused by the electron charge, via Coulomb repulsion (space charge), and rest mass, via vacuum dispersion of the electron wavefunction. Space charge effects and a finite energy bandwidth both lead to temporal broadening of electron pulses. Methods to compress such pulses in microwave fields have been developed, but these are fundamentally limited by the achievable temporal synchronisation of the employed microwave with the excitation laser pulses. This work is aimed at breaking this limitation and thereby advancing ultrafast electron diffraction towards the ultimate temporal resolution of any realistic light--matter interaction. Firstly, a high-resolution optical-microwave phase detector based on optical interferometry is designed for operation around the 800-nm wavelength of Ti:sapphire lasers best suited for sample excitation. The phase detector provides a resolution of 3 fs and the capability of functioning as an integral component in a phase-locked loop for synchronising a low-noise dielectric resonator oscillator with the Ti:sapphire laser. Furthermore, we demonstrate a separate, novel, passive synchronisation technique through direct microwave extraction of a harmonic of the laser repetition rate by photodetection. A record-low residual phase noise over nine frequency decades (mHz--MHz) is achieved through implementation of an optical-mode filter which circumvents thermal noise problems at low pulses energies to simultaneously reduce detrimental amplitude-to-phase noise conversion in the photodetection process. An amplification chain is designed to achieve a microwave power suitable for electron compression while preserving this excellent phase noise. Rigorous out-of-loop characterisation of the synchronisation with the optical-microwave phase detector shows a root-mean-square (rms) timing stability of 4.8 fs. This superior synchronisation has allowed the generation of 12 fs (rms) electron pulses, the shortest to our knowledge. Lastly, stability of the laser--electron synchronisation over many hours is also demonstrated on a sub-five-femtosecond scale through in-situ measurement and subsequent compensation for the entire range of possible long-term drifts. This shows that incorporating these techniques can allow ultrafast electron diffraction experiments to observe the fastest reversible atomic-scale light--matter interaction dynamics.

In this thesis we study geometric corrections to the low-energy effective actions of string theory. More concretely, we compute higher-derivative corrections to the couplings of three-dimensional, N = 2 supergravity theories and interpret the induced α′-corrections in N = 1, minimal supergravity theories in four dimensions, in the framework of F-theory. These allow for chiral spectra and are therefore phenomenological relevant. We analyzed higher-derivative corrections to M-theory, accessible through its low-energy effective theory, given by eleven-dimensional supergravity. The next to leading order terms to eleven-dimensional supergravity carry eight-derivatives, and are suppressed by lM6 compared to the classical terms, with lM being the eleven-dimensional Planck-Length - the only scale in eleven dimensions. These corrections are lifted from IIA supergravity corrections, which are derived from string scattering amplitudes. The common theme of this thesis is to compactify the bosonic sector of the eleven-dimensional supergravity action, including all known eight-derivative corrections, on a supersymmetric background to find a 3d, N = 2 theory, which then can be lifted to a 4d, N = 1 theory. This goal is approached in several steps. In the classical reduction of eleven-dimensional supergravity the metric background is a direct product of the external space, consisting of two space and one time dimension and the internal eight spacelike-dimensional Calabi-Yau manifold. However, when considering higher-derivative corrections the background has to be altered by introducing a dependence of the external space on the warp- factor, which is a function of the internal space. We find an explicit warped background solution to the eleven-dimensional E.O.M.’s including non-vanishing flux. To check the background for its supersymmetry features one would need to consider the eleven-dimensional gravitino variations at this order in lM . However, these are not known, which leads us to propose higher-order lM -corrected gravitino variations consistent with our background solution. As a next step we dimensionally reduce the bosonic sector of the eleven-dimensional supergravity action including all eight-derivative terms on this warped background and analyze the resulting three- dimensional theory. In this context the interplay of the warp-factor and the higher-derivative terms is of crucial importance. To identify the N = 2 properties of the resulting three-dimensional theory obtained by dimensional reduction, we compare it to the canonical from of three-dimensional N = 2 supergravtiy. We conclude that the reduced action is compatible with N = 2 supersymmetry and give a proposal for the K ̈ahler potential and the complex coordinates, which receive lM6 corrections. Besides a warp-factor contribution, the K ̈ahler potential receives a correction proportional to the third Chern- 2 form of the zeroth order internal background, being the Calabi-Yau fourfold. The complex coordinates are defined as divisor-integrals and are corrected by a warp-factor dependent term as well as one related to the non-harmonic part of the fourth Chern-form, of the zeroth order Calabi-Yau manifold. Thus the couplings of the resulting theory receive besides the warp-factor, in particular geometric corrections of order lM6 . In the first part of this thesis we study a simplified setup, only considering a subset of the relevant eight-derivative corrections in eleven dimensions. Furthermore, we do compactify on the classical background, consisting of the internal Calabi-Yau fourfold without warping and fluxes, to gain a three-dimensional theory. However, we use the M/F-theory duality to uplift the yielded corrections, which results in corrections to the couplings of the four-dimensional theory. In the weak coupling limit we find that these are sourced by the self-intersection curves of D7-branes.

The highly successful Belle experiment was located at the KEKB accelerator in Tsukuba, Japan. KEKB was an electron-positron ring accelerator running at the asymmetric energies of 8 GeV (e-) and 3.5 GeV (e+). The Belle experiment took data from 1999 to 2010, but was shut down in June 2010 in order to begin a major upgrade of the accelerator and the detector. Belle played a crucial role in the award of the 2008 Nobel Prize for Physics to M. Kobayashi and T. Maskawa. The main physics goal of Belle was the measurement of CP-violation in the B-meson system. This mission, as well as the search for physics beyond the Standard Model, has been passed to the Belle II experiment located at the SuperKEKB accelerator, the direct successors of the Belle experiment and KEKB respectively. The precise measurement of CP-violation and the search for rare or "forbidden" decays of the B-meson and the tau-lepton as signals for New Physics relies heavily on a large number of recorded events and the precision with which B-meson and lepton decay vertices can be reconstructed. Thus, the accelerator upgrade aims for an increase of the luminosity by a factor of 40, resulting in a peak luminosity of 8x10^35 cm^{-2} s^{-1}. This upgrade is scheduled to be finished by 2017 and will result in asymmetric beam energies of 7 GeV (e-) and 4 GeV (e+), provided by beams with a vertical size of only 48 nm ("nano-beam optics"), a size that has never been reached at any particle collider before. The accelerator upgrade will result in the desired increase of the collision rate of particles, while it will also inevitably lead to an increase in the background for all sub-detectors. The Belle detector would not have been able to handle the new background conditions expected at SuperKEKB, hence an upgrade of the Belle detector to the Belle II detector was necessary. Additionally the upgrade aims to increase the physics performance of the detector, making it more sensitive to the effects of New Physics. The detector upgrade will see improvements and redesigns of almost all subsystems as well as the inclusion of a whole new sub-detector, the PiXel vertex Detector (PXD). The introduction of the PXD will ensure that decay vertices are reconstructed with an extremely high precision in the harsh background conditions expected at Belle II. The PXD is a semi-conductor based particle tracking detector and will be the innermost sub-detector of Belle II. It offers excellent track and vertex reconstruction capabilities, while having a thickness of only 75 μm in order to minimise multiple scattering effects. Due to the innovative concept of a high-luminosity nano-beam accelerator, the scale of background being produced at the future SuperKEKB cannot be derived from a traditional electron-positron collider and has, therefore, to be simulated using first-principle Monte Carlo techniques. This thesis focuses on a detailed study of the expected background for the pixel vertex detector at the upcoming Belle II experiment. It starts with a comprehensive summary of the key components of the SuperKEKB accelerator and the Belle II detector before delving into the details of the Belle II simulation and reconstruction framework basf2. It was decided to develop the basf2 framework from scratch, rather than adapting the software framework used at Belle. The changes made in the upgrade from the Belle to the Belle II detector, would have required major modifications of nearly all existing libraries. This thesis continues by explaining, in detail, the measurement and analysis of an experiment conducted at Belle in 2010, shortly before the KEKB accelerator and the Belle detector were shut down. The experiment aimed at establishing the validity of a major background for the PXD, namely the two-photon process into an electron-positron pair, described by the Monte-Carlo generators KoralW and BDK, which have never been tested in the kinematical region relevant for the PXD. From a comparison based on Monte Carlo data it is found that the difference between KoralW and BDK in the high cross-section, low pt region (smaller than 20 MeV) for the produced electron and positron is very small, and that both Monte-Carlo generators agree with the experiment in this important low momentum regime. However, the question arises as to whether the delivered cross-section of the Monte Carlo generators is correct over a wider phase space, but still below the centre-of-mass energies where these generators have been verified experimentally (e.g. at the e+e- colliders PETRA and LEP). In order to answer this question, a comparison between recorded detector data and Monte Carlo data is performed, an analysis that has never been done for centre-of-mass energies of the order of those of the Belle and Belle II experiments. From the results the conclusion is drawn that both Monte Carlo generators, KoralW and BDK, agree very nicely for low values of pt but differ significantly for intermediate values where the total cross-sections are already very small. The recorded data proved that for intermediate pt ranges the behaviour of BDK is correct, while KoralW overshoots the data. Since, however, the cross-section peaks strongly for low values of pt both generators can be used for further background studies. Furthermore, this thesis includes a detailed basf2 simulation study of the major beam and QED backgrounds that are expected at Belle II and their impact on the PXD. Various figures of merit are estimated, such as particle flux, radiation dose and occupancy. On average the inner layer experiences a particle flux of 6.1 MHz cm^{-2} and the outer layer of 2.5 MHz cm^{-2}. The distribution of the particle flux along the global z-axis is fairly flat meaning that the radiation damage is evenly distributed along the PXD ladders. The simulation shows that the inner layer of the PXD is exposed to a radiation dose of 19.9 kGy/smy and the outer layer to a dose of 4.9 kGy/smy. Irradiation tests of DEPFET sensors with 10 MeV electrons showed that the sensors work reliably for a dose of at least 100 kGy. It is believed that they can even cope with up to 200 kGy. Using the radiation dose values obtained from the simulation, the numbers translate to a lifetime of roughly 10 years for the PXD sensors, the typical operation time of a high energy physics detector. The study shows that the expected PXD occupancy, summing over all background sources, is given by inner layer: 1.28 +- 0.03 % outer layer: 0.45 +- 0.01 % The upper limit for the PXD, imposed by the data acquisition and the track reconstruction, is 3%. The estimated values are well below this limit and, thus, the PXD will withstand the harsh background conditions that are expected at Belle II.

Gewitterzellen mit ihren negativen Begleiterscheinungen wie Starkregen, Hagel oder Fallwinden verursachen Verspätungen sowie Flugausfälle und sind damit für höhere Kosten der Airlines und Flughafenbetreiber verantwortlich. Eine verlässliche Vorhersage von Gewittern bis zu mehreren Stunden könnte dagegen den Entscheidungsträgern am Flughafen einen größeren zeitlichen Spielraum geben, um auf mögliche Gewitterzellen angemessen zu reagieren und adäquate Maßnahmen zu ergreifen. Zur Bereitstellung zuverlässiger Gewittervorhersagen bis zu sechs Stunden wurde Cb-LIKE am Deutschen Zentrum für Luft- und Raumfahrt (DLR) entwickelt. Der neue Gewittervorhersagealgorithmus wird in der vorliegenden Dissertation detailliert vorgestellt. Cb-LIKE ist ein automatisiertes System, das unter Verwendung von Modelldaten des COSMO-DE Wettermodells des Deutschen Wetterdienstes (DWD) Gebiete ausweist, die eher für oder gegen eine Entwicklung von Gewittern sprechen. Vier atmosphärische Parameter (CAPE, Vertikalwind, Radarreflektivität und Temperatur an der Wolkenobergrenze) fließen in das System ein. Eine neu entwickelte „Best-Member-Selection“ sorgt dabei durch einen Abgleich zur aktuellen Gewittersituation für die automatische Auswahl des realistischsten Modelllaufes aus einem Ensemble. Dadurch wird die beste Datengrundlage für die Berechnung der Gewittervorhersagen gewährleistet. Für die Auswahl des besten Members stehen vier verschiedene Modi zur Verfügung. Ein neu entwickeltes Fuzzy-Logik System ermöglicht anschließend die Kombination der Modelldaten und die Berechnung eines Gewitterindikators von 11,6¯6 bis 88,3¯3 für jeden Gitterpunkt des Modells für die nächsten sechs Stunden in stündlichen Intervallen. Je höher der Wert des Indikators, desto mehr sprechen die Modellparameter für die Entstehung von Gewittern. Zusätzlich wird die Vorhersagequalität des neuen Algorithmus anhand einer umfassenden Verifikation unter Verwendung einer „neighbourhood-verification“ Technik und von „multi-event contingency tables“ untersucht. Für die Sommerperiode 2012 weist Cb-LIKE im Vergleich zur COSMO-DE Radarreflektivität bessere Werte in den Verifikationsgrößen auf. So ist das „Fehlalarmverhältnis“ für den neuen Algorithmus niedriger (0,48 zu 0,56), die „Wahrscheinlichkeit der Detektion“ (0,52 zu 0,45) und der „Critical Success Index“ (0,50 zu 0,48) fallen dagegen höher aus. Die Resultate zeigen, dass der Cb- LIKE Algorithmus eine sinnvolle neue Methodik für Gewittervorhersagen von hoher Qualität auf der Datenbasis des COSMO-DE Modells darstellt. Die Ergebnisse aus der Verifikation ermöglichen außerdem die Übersetzung des Cb-LIKE Indikatorfeldes in die gewünschten probabilistischen Gewittervorhersagen. Zusätzlich wird die erfolgreiche Implementierung der Cb-LIKE Gewittervorhersagen in das WxFUSION System, eine graphische Benutzeroberfläche, vorgestellt.

This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. All observables arising from those dynamics match on certain families of background space times. These different backgrounds are connected by T-duality. DFT renders T-duality on a torus manifest by adding D windig coordinates in addition to the D space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for fields which depend on half of the coordinates of the arising doubled space. An important application of DFT are generalized Scherk-Schwarz compactifications. They give rise to half-maximal, electrically gauged supergravities which are classified by the embedding tensor formalism, specifying the embedding of their gauge group into O(n,n). Because it is not compatible with all solutions of the embedding tensor, the strong constraint is replaced by the closure constraint of DFT's flux formulation. This allows for compactifications on backgrounds which are not T-dual to well-defined geometric ones. Their description requires non-geometric fluxes. Due to their special properties, they are also of particular phenomenological interest. However, the violation of the strong constraint obscures their uplift to full string theory. Moreover, there is an ambiguity in generalizing traditional Scherk-Schwarz compactifications to the doubled space of DFT: There is a lack of a general procedure to construct the twist of the compactification. After reviewing DFT and generalized Scherk-Schwarz compactifications, DFT_WZW, a generalization of the current formalism is presented. It captures the low energy dynamics of a closed bosonic string propagating on a compact group manifold and it allows to solve the problems mentioned above. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constraint, while for the former the closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the traditional formulation, DFT_WZW is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the traditional formulation is restored. A flux formulation for the new theory is derived and its connection to generalized Scherk-Schwarz compactifications is discussed. Further, a possible tree-level uplift of a genuinely non-geometric background (not T-dual to any geometric configuration) is presented. Finally, the ambiguity in constructing the compactification's twist is eliminated. Altogether, a more general picture of DFT and the structures it is based on emerges.

This thesis presents a study of the galaxy populations in massive galaxy clusters that have been selected via the Sunyaev - Zeldovich Effect from the South Pole Telescope. The clusters have multiband optical imaging data from the Dark Energy Survey (DES). Each cluster has a robust mass estimate and with the deep DES data they cover a redshift range between 0 and 1.1. This makes it an ideal cluster sample to study evolutionary trends of the galaxy populations with mass and redshift.