Die satellitengestützte Radarinterferometrie liefert Informationen zu vertikalen Bodenbewegungen in hoher raum-zeitlicher Auflösung. Moderne Auswerteverfahren in Kombination mit hochauflösenden Sensoren ermöglichen die Anwendung dieser Monitoringmethode auf Tagebaukippen. Die damit verfügbare Datenbasis erlaubt eine flächenhafte Analyse des Setzungsverhaltens der Oberfläche der Tagebaukippe und erweitert damit die bisherige punktartige Betrachtung unter Nutzung von Höhenfestpunkten. Der vorliegende Beitrag demonstriert, wie aus den räumlich verteilten Zeitreihen eine flächenhafte Modellierung des Zeitsetzungsverhaltens von Tagebaukippen erfolgen kann. Dazu werden klassische Modelle des Zeitsetzungsverlaufes auf die Ergebnisse der satellitengestützten Radarinterferometrie angewandt. Im Ergebnis kann geschlussfolgert werden, dass das hier vorgestellte Verfahren eine nahezu rein datengetriebene Prognose von wichtigen Indikatoren, wie z. B. Zeit bis zum Abklingen der Setzung oder zu erwartende maximale Setzung, erlaubt. Weiterhin liefert das Verfahren eine reiche Datengrundlage zur detaillierten Untersuchung weitere Einflussfaktoren auf das Setzungsverhalten von Tagebaukippen.

LISA, the Laser Interferometry Space Antenna, is the 3rd large mission (L3) of the ESA program Cosmic Vision with a junior partnership from NASA planned to be launched around 2034. Space-based gravitational wave observatories such as LISA have been developed for observation of sources that produce gravitational wave (GW) signals with frequencies in the mHz regime. The frequency band is achievable by having a longer-baseline interferometer compared to ground-based detectors. In addition, the significant size of the LISA arms-length guarantees the detection of many astrophysical sources. The absence of Newtonian noise in space, which is the dominant source of noise below few hertz for ground-based detectors, allows LISA to be sensitive to lower frequency compared to the former. Thus, going to space allows studying different sources with respect to the ones of interest for ground-based detectors such as supermassive black holes. Although having very long baselines between the satellites generally increases the sensitivity to gravitational waves, it also implies many technical challenges, such that a balance must be found between scientific performance and technical feasibility.In the actual proposal LISA is designed to be a constellation of three identical spacecraft in a triangular formation with six active laser links connecting the three spacecraft, which are separated by 2.5 million km. To fulfil the observatory program every spacecraft has a minimum requirement of two free-falling test masses, two telescopes, and two lasers. The detector’s center-of-mass follows a circular, heliocentric trajectory, trailing 20 degrees behind the Earth and the plane of the detector is tilted by 60 degrees with respect to the ecliptic.The goal of LISA is to detect GWs which manifest themselves as a tiny fluctuation in the frequency of the laser beam measured at the phase-meter. Thus, to detect GW you need to compete with many sources of disturbance that simulate the effect of a GW frequency modulation. Laser noise is an example of those. Therefore, one key element in the LISA data production chain is the post-processing technique called Time Delay Interferometry aimed at suppressing the intense laser frequency noise that would completely cover the astrophysical signal. Data from the six independent inter-satellite links, connecting the three spacecraft, are properly time-shifted and combined to form the final scientific signal. This post-processing technique circumvents the impossibility of physically building in space an equal arm interferometer, which would intrinsically beat the frequency noise by comparing light generated at the same time.The following work is focused on revisiting the Time-Delay-Interferometry (TDI) for LISA and studying the usage of all the possible TDI combinations we can build for the LISA instrument characterisation and science extraction. Many possible TDI combinations that suppress the frequency noise have been identified in the past and this thesis revisits the TDI technique focusing on the physical interpretation of it, that is a virtual interference of photons that have been travelling through the constellation via different paths but performing the same total distance. We illustrate all possible TDI configurations that suppress the laser noise contribution to the level required by the mission to understand how TDI channels can be best used for the diagnostic of the instrument and LISA science. With this philosophy, we develop an algorithm to search for all possible combinations that suppress laser noise at the same level as the classical TDI X, Y, and Z combinations presented in the TDI literature. This algorithm finds new combinations that fulfill the noise suppression requirement as accurately as X, Y, and Z.The LISA mission has been also advertised to probe the early Universe by detecting a stochastic GW background. Once the laser frequency noise has been subtracted, the stochastic signal, both cosmological and astrophysical, is itself going to contribute to the noise curve. Therefore it is necessary to have a good estimate of the noise of the instrument to discriminate between the stochastic background signal and the LISA noise.The strategy that has been suggested in the literature is to use the TDI T, insensitive (up to a certain order) to GW signals to estimate the pure instrumental noise in order to distinguish between the LISA background noise and the GW stochastic signal. Following this idea, as instrument noise is expected to have multiple, independent sources, this thesis explores combinations that could allow discriminating among those sources of noise, and between them and the GW signal, with the purpose of understanding how we can characterise our instrument using TDI. We illustrate special TDI combination signals in LISA, in addition to TDI T, that we call null-channels, which are ideally insensitive to gravitational waves and only carry information about instrumental noise. Studying the noise properties that can be extracted by monitoring these interferometric signals, we state that individual acceleration noise parameters are not well constrained. All null-channels behave as an ideal Sagnac interferometer, sensitive just to a particular linear combination of the six test masses acceleration that resembles a rotational acceleration signal of the entire constellation. Moreover, all null-channels show approximately the same signal to noise ratio remarkably suppressed relative to that of the TDI X. In support and application of our theoretical studies, we also give an introduction on calibrating the LISA instrument by injecting spurious signals in a LISA link and see how these propagates through a TDI channel. Indeed, this will be useful to calibrate the instrument during operations and also to build the basis for the data analysis to discriminate spurious signals from gravitational waves. My contribution to the results we present in this thesis can be summarised as the following. I supported the studies and the realisation of the search TDI algorithm whose results are published in the article. In particular, I took care of cataloging the new TDI combinations and consolidating the results we found. I have updated the TDI combinations reported in the above-mentioned work, the final version of it is reported in this thesis. I worked on the characterisation of these combinations concerning secondary noises such as clock noise, readout noise, residual laser frequency noise, and acceleration noise. In particular, I studied how these noises are transferred through the various TDI and I derive the correspondent analytical models. I then realize a software with Wolfram Mathematica, design to load and combines phase data produced by an external simulator to build the final TDI outputs, besides I also did the noise models’ validation. The basis of this program was then used to implement these TDI combinations in LISANode. Finally, I developed the algorithm to study how disturbances in force, such as glitches, and simple GW signals, such as monochromatic GW binaries, propagate through TDI and null-channels. Moreover, I tested through simulations the validity of these TDI and null-channels to distinguish instrumental artefact from GW signals and to characterise the instrumental noise.

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The Landau-Zener-Stückelberg-Majorana (LZSM) problem models diabatic transitions between energy levels in quantum two-level systems with an avoided level-crossing. The diabatic transition is a consequence of quantum tunneling in energy space when the system's Hamiltonian is perturbed with a fast-acting bias. The probability of transition between the energy states for a linear bias is known as the LZSM transition probability. The objective of this work is to investigate the LZSM problem through analytical and numerical lenses. The LZSM transition probability is derived in two ways. The first approach is based on Majorana's solution using contour integrals. The second derivation follows Landau's quasi-classical treatment. The derivations demonstrate methods for transitions in the presence of time-dependent perturbations. The ubiquity of the two-level system is discussed and an application on qubits concerning LSZM interferometry is presented, with the latter arising after considering periodic biases. Lastly, a simulation of the two-level system is conducted using Trotter-decomposed time-evolution operators, perturbation theory, and vectorization. The simulated transition probabilities for linear and periodic biases are obtained for varied parameters. The results show that the simulation achieves an accurate and efficient emulation of the LZSM problem.

No / PURPOSE: To estimate refractive indices used by the Lenstar biometer to translate measured optical path lengths into geometrical path lengths within the eye. METHODS: Axial lengths of model eyes were determined using the IOLMaster and Lenstar biometers; comparing those lengths gave an overall eye refractive index estimate for the Lenstar. Using the Lenstar Graphical User Interface, we noticed that boundaries between media could be manipulated and opposite changes in optical path lengths on either side of the boundary could be introduced. Those ratios were combined with the overall eye refractive index to estimate separate refractive indices. Furthermore, Haag-Streit provided us with a template to obtain 'air thicknesses' to compare with geometrical distances. RESULTS: The axial length estimates obtained using the IOLMaster and the Lenstar agreed to within 0.01 mm. Estimates of group refractive indices used in the Lenstar were 1.340, 1.341, 1.415, and 1.354 for cornea, aqueous, lens, and overall eye, respectively. Those refractive indices did not match those of schematic eyes, but were close in the cases of aqueous and lens. Linear equations relating air thicknesses to geometrical thicknesses were consistent with our findings. CONCLUSION: The Lenstar uses different refractive indices for different ocular media. Some of the refractive indices, such as that for the cornea, are not physiological; therefore, it is likely that the calibrations in the instrument correspond to instrument-specific corrections and are not the real optical path lengths.

Atom Interferometrie ist eine sehr genaue und sensitive Methode mit einer Vielzahl von Anwendungsmöglichkeiten, zu der auch die Messung der Erdbeschleunigung zählt. Während die meisten Atom Interferometer aus großen, ortsfesten Aufbauten bestehen, werden auf diesem Gebiet häufig mobile Messgeräte benötigt. Das Gravimetric Atom Interferometer (GAIN) Projekt wurde ins Leben gerufen, um dieser zusätzlichen Anforderung bei bestmöglicher Messgenauigkeit gerecht zu werden. Es soll eine Alternative zu anderen modernsten Gravimetertypen geschaffen werden, die wichtige funktionale Eigenschaften wie eine hohe Auflösung und absolute Genauigkeit in einem Gerät vereint. Der GAIN Sensor verwendet lasergekühlte Rb87 Atome in einer 1 m hohen Fontäne. Mit Hilfe von stimulierten Raman Übergängen wird ein beschleunigungssensitives Interferometer realisiert. In dieser Arbeit wurde der Sensor mit Blick auf mobile und driftfreie Langzeitmessungen weiterentwickelt. Dafür wurden einzelne Subsysteme des Laseraufbaus auf die daraus resultierenden Anforderungen hin angepasst oder neu entwickelt. Mit derselben Zielstellung wurden weiterhin systematische Effekte in dem Messaufbau untersucht und Maßnahmen für ihre Reduzierung realisiert. Der Aufbau wurde transportiert und in relevanten Umgebungen getestet. Dabei konnte gezeigt werden, dass die Leistungsfäigkeit dieses Aufbaus mit denen der wichtigsten und modernsten Gravimeter konkurieren kann, sie teilweise übertrifft und dass dieser Sensor zur präzisen Kalibrierung der relativen Gravimeter verwendet werden kann. In den Messungen wurde eine Sensitivität von 138 nm/s^2/Sqrt(Hz) sowie eine Langzeitstabilität von 5 x 10^−11 g über 10^5 s erreicht. / Atom interferometry offers a very precise and sensitive measurement tool for various areas of application whereof one is the registration of the gravity acceleration. While the vast majority of atom interferometers include large and stationary setups, this field very often implies the additional request for a mobile apparatus. The Gravimetric Atom Interferometer (GAIN) project has been started to meet this requirement and to provide best possible accuracy at the same time. It aims to realize an alternative to other types of gravimeters and to combine important qualities such as high sensitivity and absolute accuracy in one instrument. The GAIN sensor is based on laser-cooled Rb87 atoms in a 1 m atomic fountain. Stimulated Raman transitions form a Mach-Zehnder type interferometer which is sensitive to accelerations. In this work it has been advanced to meet all requirements for mobile and drift-free long-term operation. Therefore, selected parts of the laser system have been improved or redeveloped. A second focus has been on systematic effects for the same objective. They have been analyzed and measures for their suppression have been undertaken. The apparatus has been transported, tested in relevant environments, and compared to the most important state-of-the-art gravimeter types where a competitive performance has been achieved. It is demonstrated, that the gravity signal of this sensor allows for a precise calibration of the relative gravimeter types. During the measurements a best sensitivity of 138 nm/s^2/Sqrt(Hz) and a stability of 5 x 10^−11 g after 10^5 s has been reached.

Quantensensoren, wie Atominterferometer und Atomuhren werden zu hochpräzisen und akkuraten Messungen von Inertialkräften und der Zeit benutzt und sind hervorragend dazu geeignet fundamentale Fragestellungen der Physik anzugehen und die Aussagen der allgemeinen Relativitätstheorie zu testen. Die Empfindlichkeit von Atominterferometern skaliert quadratisch mit der freien Entwicklungszeit und die Verwendung von Quantensensoren im Weltraum ist prädestiniert die Genauigkeit von Tests des Äquivalenzprinzips um mehrere Größenordnungen zu verbessern. Zusätzlich, werden präzise und akkurate Sensoren für Inertialkräfte, im Bereich der Navigation oder Geodäsie benutzt wo mobile auf Atominterferometrie basierende Geräte noch selten sind. Diese Arbeit trägt zur Entwicklung von hochempfindlichen und stabilen mobilen Quantensensoren bei. Im Rahmen dieser Doktorarbeit wurden drei mobile Vergleichsmessungen der Erdbeschleunigung mit dem Atominterferometer GAIN an verschiedenen geographischen Orten durchgeführt. Die demonstrierte Stabilität von 5*10^-11 g nach 10^5 s übertrifft die Stabilität von klassischen Gravimetern. Mit dem Ziel von Weltraumgestützten Atominterferometern wurde ein kompaktes Lasersystem für den Betrieb von Atominterferometrie mit Rubidium Bose-Einstein Kondensaten auf Höhenforschungsraketen entworfen, qualifiziert und in Betrieb genommen. Zusätzlich wurden drei Nutzlasten für dein Einsatz auf Höhenforschungsraketen realisiert um die Reife der notwenigen Subsysteme zu zeigen. Dopplerfreie Laserspektroskopie an Rubidium und Kalium wurde verwendet um eine optische Frequenzreferenz zu realisieren und während der Flüge wurde mit einem Frequenzkamm zu vergleichen. Diese Messung stellt einen ersten Test der Lokalen Lorenz Invarianz im Weltraum dar. Diese Aktivitäten ebnen den Weg für den zukünftigen Einsatz von Quantensensoren im Weltraum die noch nie dagewesene Tests der fundamentalen Physik, Weltraumgeodäsie oder sogar Gravitationswellen ermöglichen. / Quantum sensors, such as atom interferometers and atomic clocks are used for high precision and accurate measurements of inertial forces and time and are therefore ideally suited to address fundamental questions in physics and to test the predictions of general relativity. The sensitivity of atom interferometers scales quadratically with the free evolution time and the use of quantum sensors in space is predestined to improve the accuracy of such tests by several orders of magnitude. Additionally, precise and accurate sensors for inertial forces are required in the field of navigation or geodesy where mobile devices based on atom interferometry are still rare. This work contributes to the development of highly sensitive and stable mobile quantum sensors. In the course of this thesis, three measurement comparisons of the gravitational acceleration with the mobile atom interferometer GAIN were performed at different geographic locations. The demonstrated stability of 5*10^-11 g after 10^5 s surpasses the one reached by classical gravimeters. With the goal of space-born atom interferometry, a compact laser system for operation of atom interferometry with Bose-Einstein condensates of rubidium on a sounding rocket was designed, qualified and put in operation. Additionally, three sounding rocket payloads were realized to show the technological maturity of the necessary subsystems. Doppler-free laser spectroscopy of rubidium and potassium was used to realize an optical frequency reference that was compared during the flights to an atomic microwave standard via a frequency comb. This measurement represents the first test of the Local Position Invariance in space. These activities pave the way for future deployment of quantum sensors in space enabling unprecedented tests of fundamental physics, space geodesy or even gravitational wave detection.