Cette thèse a pour objet l’étude des effets de cohérence de la propagation d’ondes en milieu désordonné, à l’aide d’atomes ultrafroids. Ces systèmes permettent un contrôle précis de paramètres clés, tels que la dimensionnalité, les interactions, la vitesse initiale des atomes et le potentiel externe. Utilisant cette flexibilité, il a été possible de réaliser des expériences en régime fortement et faiblement localisé. La première expérience traite de l’expansion d’un condensat, dont une fraction maximale de 20% est localisée, permettant ainsi l’observation de la localisation d’Anderson en 3D. Lors de la seconde expérience, les atomes ont été envoyés dans un désordre quasi 2D avec une vitesse initiale bien définie. Il a été possible d’observer la distribution en impulsions des atomes, et ainsi de mesurer le temps de libre parcours moyen et le temps de transport. La rétrodiffusion cohérente s’est clairement manifestée sous la forme d’un pic dans la direction opposée à la direction initiale. L’amplitude et la largeur de ce pic ont été étudiées, et les résultats sont en accord avec la théorie. Microscopiquement, la rétrodiffusion cohérente a pour origine l’interférence constructive entre chemins à diffusions multiples symétriques par renversement du temps (symétrie T). Cette symétrie de la propagation d’ondes a été ensuite manipulée. Un déphasage précis a été introduit grace à un pulse de gradient de champ magnétique, qui détruit la symétrie T ainsi que la rétrodiffusion cohérente, sauf pour un bref instant : une résurgence du pic est alors observée. Ce nouvel effet démontre explicitement le rôle de la cohérence et de la symétrie T dans la localisation faible. / In this manuscript the coherence effects of wave propagation in disordered potentials is studied. Our experiment uses ultracold atoms as a probe, a system allowing for a very good control over parameters such as the dimensionality, interactions, initial velocity of the atoms, and the potential landscape. Exploiting this flexibility we were able to perform experiments in the strongly and the weakly localized regime. In the former the 3D expansion of a BEC was monitored in real space, resulting in the observation of 3D Anderson localization with a maximum localized fraction of about 20%. In the latter the atoms were launched into a quasi-2D disorder with a well defined initial velocity. Monitoring the momentum space distribution the mean scattering time and the transport time can be directly measured, and coherent backscattering (CBS) is clearly visible as a peak in the backwards direction. In a first set of experiments the evolution of the CBS amplitude and width were recorded and found to be in good agreement with theory. Microscopically, CBS stems from the constructive interference of time-reversed multiply scattered paths. In a second set of CBS experiments we manipulated the time-reversal symmetry (TRS) of the wave propagation. A surgical dephasing was introduced via a shortly pulsed gradient field, which brakes TRS and suppresses CBS except for a brief moment, when a revival of CBS is observed. This novel effect showcases explicitly the role of coherence and TRS in Coherent Backscattering and weak localization.

Cette thèse est consacrée aux progrès récents des horloges à réseau optique au strontium du LNE-SYRTE, Observatoire de Paris. L'incertitude systématique et la stabilité des horloges optiques sont 2 ordres de grandeur meilleures que les horloges atomiques micro-ondes au cesium qui réalisent la seconde SI, bénéficiant maintenent a des applications en physique fondamentale, astronomie et géosciences. Dans un futur proche, une redéfinition de la seconde SI est attendue, quand les horloges optiques se seront révélées aussi fiables et reproductibles que les horloges a micro-ondes. La thèse présente trois étapes décisives dans cette direction. Nous présentons un fonctionnemment operation quasi-continu de nos horloges Sr pendant plusieurs semaines. Des comparaisons de fréquences locales et à distance avec diverses références de fréquence micro-ondes et optiques montrent que les horloges optiques sont reproductibles par des laboratoires independants. Nous avons démontré un premier réseau tout optique entre des horloges optiques à l'échelle continentale. Les horloges au Sr ont été utilisées pour préparer 5 rapports de calibration du Temps Atomique International (TAI) qui ont été validés par le BIPM comme première contribution au TAI par des horloges optiques. Certains de ces résultats ont été utilisés pour borner l'amplitude d'une possible violation de l'invariance de Lorentz analysant les comparaisons d'horloges distantes. Enfin, nous avons effectué une caractérisation complète des déplacements de fréquence associés aux sources laser à semiconducteur utilisées pour le piégeage des atomes dans l'optique d'applications pour des horloges transportables et spatiales. / This thesis describes the latest progresses regarding the Sr optical lattice clocks at LNE-SYRTE, Observatoire de Paris. Nowadays, the systematic uncertainty and stability of optical clocks are 2 orders of magnitude better than cesium microwave fountains currently realizing the SI second, with applications in fundamental physics, astronomy and geoscience. In the near future, a re-definition of the SI second is expected, once optical clocks are proven to be as reliable and reproducible as their microwave counterparts. The thesis presents three decisive steps in this direction. First, we demonstrate nearly continuous Sr clocks over several weeks. Second, local and remote frequency comparisons against various microwave and optical frequency standards show that OLCs are reproducible over time, and by independent laboratories. We notably demonstrated the first all-optical agreement between optical clocks at continental scale. Third, the Sr clocks were used to calibrate the Temps Atomique International (TAI). The five calibration reports, which we produced, were validated by the BIPM, as the first contribution to TAI with optical clocks. In addition, some of these results were used to improve bounds on a putative violation of the Lorentz invariance by testing the stability of the frequency ratio between remote clocks. Finally, we conducted a full characterization of the frequency shifts associated with semi-conductor laser sources for the trapping light, including optical measurements and frequency shifts measurements, with applications for transportable and space clocks.

Le travail présenté dans ce manuscrit porte sur l'avancement de l'expérience FORCA-G (FORce de CAsimir et Gravitation à courte distance) dont le but est la mesure par interférométrie atomique de forces à courte distance entre un atome, piégé dans un réseau optique vertical, et une surface. Réalisée à l'aide de transitions Raman stimulées, la séparation spatiale et cohérente des paquets d'onde atomique sur des puits adjacents du réseau permet de mesurer, après recombinaison, la différence d'énergie entre ces puits, liée à l'incrément d'énergie potentielle de pesanteur : la fréquence de Bloch nB. Pour de faibles densités atomiques, il est démontré une sensibilité court terme à 1 s de dn/nB = 1,8.10-6 à l'état de l'art des capteurs de forces à atomes piégés. La mise en place d'un système de refroidissement évaporatif, afin d'augmenter le nombre d'atomes par puits, permet désormais d'explorer des régimes de fortes densités atomiques où les interactions ne peuvent être négligées. Pour des densités de 1011-1012 at/cm3, il est montré qu'un phénomène d'auto-synchronisation des spins entre en compétition avec le mécanisme d'écho de spin. L'impact de ce phénomène sur le contraste et la fréquence mesurée est étudié dans un interféromètre où les deux paquets d'onde occupent le même puits. Des premières mesures sont ensuite effectuées dans le régime où les paquets d'onde sont séparés. Elles montrent un comportement différent qui reste à modéliser. Enfin, il est montré que le protocole de mesure permet de s'affranchir des biais collisionnels : les interactions atomiques limitent la sensibilité du capteur de force sans limiter son exactitude. / This thesis presents the recent progress on the FORCA-G (FORce de CAsimir et Gravitation à courte distance) experiment which aims at measuring short range forces between an atom, trapped in a vertical optical lattice, and a mirror. Stimulated Raman transitions are used to induce coherent transport between adjacent lattice sites to perform atom interferometry in order to measure with very high sensitivity, shifts in the Bloch frequency nu_B, which is the potential increment between two lattice sites. For low atomic densities, we demonstrate a local force sensor with state-of-the art relative sensitivity on the Bloch frequency of deltanu/nu_B= 1.8x10-6 at 1 s. The recent use of evaporative cooling, in order to increase the number of atoms per well, allows to work the experiment with much denser atomic clouds where atom interactions cannot be neglected. At densities of 1011-1012 at/cm3, it is shown that a spin self-rephasing mechanism competes with the spin-echo technique. The impact of the former mechanism onto the contrast and the measured frequency is studied in an interferometer where the two partial wave packets perfectly overlap. First measurements are then performed in a regime where the two partial wave packets are spatially separated. They show a different behaviour that remains to be modelled. Finally, it is shown that the measurement protocol allows to greatly reduce collisional shifts: atom interactions limit the sensitivity of the local force sensor without limiting its accuracy.

<p>The development of ultracold atom physics enables people to study fundamental questions in quantum mechanics within this highly-tunable platform. This dissertation focuses on several topics of the dynamical evolution of quantum systems.</p><p>Chapter 2 and 3 talk about Loschmidt echo, a simple quantity that reveals many hidden properties of a system’s time evolution. Chapter 2 looks for vanishing Loschmidt echo in the complex plane of time and the corresponding dynamical quantum phase transitions (DQPT) in the thermodynamic limit. For a two-site Bose-Hubbard model consisting of weakly interacting particles, DQPTs reside at the time scale inversely proportional to the interaction, where highly entangled pair condensates also show up. Chapter 3 discusses the revival of Loschmidt echo in a discrete time crystal, a Floquet system whose discrete temporal transition symmetry is spontaneously broken. We propose a new design and demonstrate its robustness against the fluctuations in the driving field. It can also be used in precision measurement to go beyond the Heisenberg limit. Experimental schemes are presented.</p><p>Out-of-time-order correlator (OTOC) is a more complicated variant of Loschmidt echo. Experimentally it requires reversing the time evolution. In Chapter 4, by exploiting the SU(1,1) symmetry of a weakly interacting BEC and connecting its quantum dynamics to a hyperbolic space, we obtain a geometric framework that enables experimentalists to manipulate the evolution with great freedom. Backward evolution is then realized effectively to measure OTOC of such SU(1,1) systems.</p><p>Chapter 5 discusses the decoherence of a spin impurity immersed in a spinor BEC. Our calculations show that by looking at the dynamics of the impurity’s reduced density matrix, the phase of the spinor BEC can be detected.</p>

<p>Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms.</p> <p>In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis.</p> <p>In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.</p> / Doctor of Philosophy (PhD)

Diese Dissertation widmet sich der theoretischen Beschreibung ultrakalter Atome in einem optischen Einschluss. Das Hauptaugenmerk liegt hierbei auf inelastischen Resonanzen, die durch die Kopplung von Schwerpunkts- und Relativbewegung durch Anharmonizitäten im externen Potenzial Zustande kommen, der Entwicklung einer Methode zur theoretischen Beschreibung von ultrakalten Wenigteilchensystemen in einem vielseitigen Einschlusspotenzial und der Quantensimulation von Attosekundenphysik mit ultrakalten Atomen. / This thesis aims for a theoretical description of ultracold trapped atoms. The main focus are resonance phenomena due to the coupling of center-of-mass and relative motion, the development of a theoretical approach to treat ultracold few-body systems in versatile trap potentials, and the quantum simulation of attosecond physics with ultracold atoms.

Les gaz d'atomes ultrafroids offrent des possibilités sans précédent pour la réalisation et la manipulation des systèmes quantiques. Le contrôle exercé sur les interactions entre particules permet d'atteindre le régime de fortes interactions, pour des espèces d'atomes à la fois fermioniques et bosoniques. Dans la limite unitaire, où la force d'interaction est à son maximum, des propriétés universelles émergent. Pour les atomes bosoniques, celles-ci comprennent l'effet Efimov, l'existance surprenante d'une séquence infinie d'états liés à trois corps. Dans cette thèse, nous avons étudiés un système de bosons unitaires. Partant des cas à deux et à trois corps, nous avons montrés que le modèle choisi capturait correctement les caractéristiques universelles de l'effet Efimov. Pour le modèle à N-corps, nous avons développé un algorithme de Monte Carlo quantique capable de réaliser les différentes phases thermodynamiques du système : gaz normal à haute-température, condensat de Bose-Einstein, et liquide d'Efimov. Un unique composant de notre modèle resterait pertinent à la limite de température infinie, à savoir la répulsion corps dur à trois corps, qui constitue une généralisation du potentiel classique entre sphères dures. Pour ce modèle, nous avons proposé une solution au problème d'empilement compact en deux et trois dimensions, fondée sur une Ansatz analytique et sur la technique de recuit simulé. En étendant ces résultats à une situation de pression finie, nous avons montré que le système présente une transition de fusion discontinue, que nous avons identifié à travers la méthode de Monte Carlo. / Ultracold atomic gases offer unprecedented possibilities to realize and manipulate quantum systems. The control on interparticle interactions allows to reach the strongly-interacting regime, with both fermionic and bosonic atomic species. In the unitary limit, where the interaction strength is at its maximum, universal properties emerge. For bosonic atoms, these include the Efimov effect, the surprising existence of an infinite sequence of three-body bound states. In this thesis, we have studied a system of unitary bosons. Starting from the two- and three-body cases, we have shown that the chosen model correctly captures the universal features of the Efimov effect. For the corresponding many-body problem, we have developed a quantum Monte Carlo algorithm capable of realizing the different thermodynamic phases in which the system may exist: The high-temperature normal gas, Bose-Einstein condensate, and Efimov liquid. A single ingredient of our model would remain relevant in the infinite-temperature limit, namely the three-body hard-core repulsion, which constitutes a generalization of the classical hard-sphere potential. For this model, we have proposed a solution to the two- and three-dimensional packing problem, based on an analytical ansatz and on the simulated-annealing technique. Extending these results to finite pressure showed that the system has a discontinuous melting transition, which we identified through the Monte Carlo method.

This thesis covers most of my work in the field of ultracold atoms loaded in optical lattices. This thesis can be divided into five different parts. In Chapter 1, after a brief introduction to the field of optical lattices I review the fundamental aspects pertaining to the physics of systems in periodic potentials and a short overview of the experiments on ultracold atoms in an optical lattice. In Chapter 2 we develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this poten¬tial, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator(MI), density-wave(DW), and supersolid (SS) phases in the plane of the chemical potential and on-site repulsion ; we present phase diagrams for representative values of , the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI ,DW ,and SSphases. We explore the implications of our study for experiments on cold-atom dipolar con¬densates in optical lattices in a confining potential. In Chapter3 we present an extensive study of Mottinsulator( MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with har¬monic traps. For this we develop an inhomogeneous mean-field theory. Our results for the BH model with one type of spinless bosons agrees quantitatively with quan¬tum Monte Carlo(QMC) simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional(3D) systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also generalize our inhomogeneous mean-field theory to study BH models with har¬monic traps and(a) two species of bosons or(b) spin-1bosons. With two species of bosons we obtain rich phase diagrams with a variety of SF and MI phases and as¬sociated shells, when we include a quadratic confining potential. For the spin-1BH model we show, in a representative case, that the system can display alternating shells of polar SF and MI phases; and we make interesting predictions for experi¬ments in such systems. . In Chapter 4 we carry out an extensive study of the phase diagrams of the ex-tended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane ¬insulator(HI) phases. We show that the critical exponents and central charge for the HI-DW,MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) uni¬versality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different bound¬ary conditions lead to different phase diagrams.. In Chapter 5 we obtain the excitation spectra of the following three generalized of Bose-Hubbard(BH) models:(1) a two-species generalization of the spinless BH model, (2) a single-species, spin-1 BH model, and (3) the extended Bose-Hubbard model (EBH) for spinless interacting bosons of one species. In all the phases of these models we show how to obtain excitation spectra by using the random phase approximation (RPA). We compare the results of our work with earlier studies of related models and discuss implications for experiments.

L’objectif principal de cette thèse est l’étude théorique de mélanges quantiques fortement interagissants à une dimension et soumis à un potentiel externe harmonique. De tels systèmes fortement corrélés peuvent être réalisés et testés dans des expériences d’atomes ultrafroids. Leurs propriétés de symétrie par permutation non triviales sont étudiées, ainsi que leurs effets sur les corrélations. Exploitant une solution exacte pour des interactions fortes, nous extrayons des propriétés générales des corrélations encodées dans la matrice densité à un corps et dans les distributions des impulsions associées, dans les mélanges fermioniques et de Bose-Fermi. En particulier, nous obtenons des résultats substantiels sur le comportement à courtes distances, et donc les queues à haute impulsions, qui suivent des lois en k^−4 typiques. Les poids de ces queues, dénotés contacts de Tan, sont liés à de nombreuses propriétés thermodynamiques des systèmes telles que les corrélations à deux corps, la dérivée de l’énergie par rapport à la longueur de diffusion unidimensionnelle, ou le facteur de structure statique. Nous montrons que ces contacts universels de Tan permettent également de caractériser la symétrie spatiale des systèmes, et constituent donc une connexion profonde entre les corrélations et les symétries. En outre, la symétrie d’échange est extraite en utilisant une méthode de théorie des groupes, à savoir la méthode de la somme des classes (class-sum method en anglais), qui provient à l’origine de la physique nucléaire. De plus, nous montrons que ces systèmes suivent une version généralisée du fameux théorème de Lieb-Mattis. Souhaitant rendre nos résultats aussi pertinents expérimentalement que possible, nous dérivons des lois d’échelle pour le contact de Tan en fonction de l’interaction, de la température et du confinement transverse. Ces lois présentent des effets intéressants liés aux fortes corrélations et à la dimensionnalité. / The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in ultracold atoms experiments. Their non-trivial permutational symmetry properties are investigated, as well as their interplay with correlations. Exploiting an exact solution at strong interactions, we extract general correlation properties encoded in the one-body density matrix and in the associated momentum distributions, in fermionic and Bose-Fermi mixtures. In particular, we obtain substantial results about the short-range behavior, and therefore the high-momentum tails, which display typical k^−4 laws. The weights of these tails, denoted as Tan’s contacts, are related to numerous thermodynamic properties of the systems such as the two-body correlations, the derivative of the energy with respect to the one-dimensional scattering length, or the static structure factor. We show that these universal Tan’s contacts also allow to characterize the spatial symmetry of the systems, and therefore is a deep connection between correlations and symmetries. Besides, the exchange symmetry is extracted using a group theory method, namely the class-sum method, which comes originally from nuclear physics. Moreover, we show that these systems follow a generalized version of the famous Lieb-Mattistheorem. Wishing to make our results as experimentally relevant as possible, we derive scaling laws for Tan’s contact as a function of the interaction, temperature and transverse confinement. These laws. Display displadisplay display interesting effects related to strong correlations and dimensionality.

Cold-atom quantum simulators offer unique possibilities to prepare, manipulate, and probe quantum many-body systems. However, despite the high level of control in modern experiments, not all observables of interest are easily accessible. This thesis aims at establishing protocols to measure currently elusive static and dynamic properties of quantum systems. The experimental feasibility of these schemes is illustrated by means of numerical simulations for relevant applications in many-body physics and quantum simulation. In particular, we introduce a general method for measuring dynamical correlations based on non-Hermitian linear response. This enables unbiased tests of the famous fluctuation-dissipation relation as a probe of thermalization in isolated quantum systems. Furthermore, we develop ancilla-based techniques for the measurement of currents and current correlations, permitting the characterization of strongly correlated quantum matter. Another application is geared towards revealing signatures of supersolidity in spin-orbit-coupled Bose gases by exciting the relevant Goldstone modes. Finally, we explore a scenario for quantum-simulating post-inflationary reheating dynamics by parametrically driving a Bose gas into the regime of universal far-from-equilibrium dynamics. The presented protocols also apply to other analog quantum simulation platforms and thus open up promising applications in the field of quantum science and technology. / I simulatori quantistici ad atomi freddi offrono possibilità uniche per preparare, manipolare e sondare sistemi quantistici a molti corpi. Tuttavia, nonostante l'alto livello di controllo raggiunto negli esperimenti moderni, non tutte le osservabili di interesse sono facilmente accessibili. Lo scopo di questa tesi è quello di stabilire protocolli per misurare delle proprietà statiche e dinamiche dei sistemi quantistici attualmente inaccessibili. La fattibilità sperimentale di questi schemi è illustrata mediante simulazioni numeriche per applicazioni rilevanti nella fisica a molti corpi e nella simulazione quantistica. In particolare, introduciamo un metodo generale per misurare le correlazioni dinamiche basato su una risposta lineare non hermitiana. Ciò consente test imparziali della famosa relazione fluttuazione-dissipazione come sonda di termalizzazione in sistemi quantistici isolati. Inoltre, sviluppiamo tecniche basate su ancilla per la misura di correnti e correlazioni di corrente, consentendo la caratterizzazione della materia quantistica fortemente correlata. Un'altra applicazione è orientata a rivelare l'impronta della supersolidità nei gas Bose con accoppiamento spin-orbita eccitando il corrispondente modo di Goldstone. Infine, esploriamo uno scenario per la simulazione quantistica della dinamica di riscaldamento post-inflazione modulando parametricamente un gas Bose e portandolo nel regime della dinamica universale lontana dall'equilibrio. I protocolli presentati si applicano anche ad altre piattaforme di simulazione quantistica analogica e aprono quindi applicazioni promettenti nel campo della scienza e della tecnologia quantistica. / Quantensimulatoren auf Basis ultrakalter Atome eröffnen einzigartige Möglichkeiten zur Präparation, Manipulation und Untersuchung von Quanten-Vielteilchen-Systemen. Trotz des hohen Maßes an Kontrolle in modernen Experimenten sind jedoch nicht alle interessanten Observablen auf einfache Weise zugänglich. Ziel dieser Arbeit ist es, Protokolle zur Messung aktuell nur schwer erfassbarer statischer und dynamischer Eigenschaften von Quantensystemen zu etablieren. Die experimentelle Realisierbarkeit dieser Verfahren wird durch numerische Simulationen anhand relevanter Anwendungen in der Vielteilchenphysik und Quantensimulation veranschaulicht. Insbesondere wird eine allgemeine Methode zur Messung dynamischer Korrelationen basierend auf der linearen Antwort auf nicht-hermitesche Störungen vorgestellt. Diese ermöglicht unabhängige Tests des berühmten Fluktuations-Dissipations-Theorems als Indikator der Thermalisierung isolierter Quantensysteme. Darüber hinaus werden Verfahren zur Messung von Strömen und Strom-Korrelationen mittels Kopplung an einen Hilfszustand entwickelt, welche die Charakterisierung stark korrelierter Quantenmaterie erlauben. Eine weitere Anwendung zielt auf die Enthüllung spezifischer Merkmale von Supersolidität in Spin-Bahn-gekoppelten Bose-Einstein-Kondensaten ab, indem die relevanten Goldstone-Moden angeregt werden. Schließlich wird ein Szenario zur Quantensimulation post-inflationärer Thermalisierungsdynamik durch die parametrische Anregung eines Bose-Gases in das Regime universeller Dynamik fern des Gleichgewichts erschlossen. Die dargestellten Protokolle lassen sich auch auf andere Plattformen für analoge Quantensimulation übertragen und eröffnen damit vielversprechende Anwendungen auf dem Gebiet der Quantentechnologie.