Emerging from the cosmic web, galaxy clusters are the most massive gravitationally bound structures in the universe. Thought to have begun their assembly at 2 < z < 3, i.e. 10 to 11 billion years ago, clusters provide insights into the growth of large-scale structure as well as the physics that drives galaxy evolution. The redshift range 1 < z < 3 is a key epoch in their evolution. At z ∼ 1.5, elliptical galaxies start to become the dominant population in cluster cores, and star formation in spiral galaxies is being quenched. But there is also evidence for a progressive increase in the amount of star formation that occurs in galaxy cluster cores at z ≳ 1.5. To understand the dependence of the formation mechanisms of massive galaxies with environment, we must focus on clusters at relatively unexplored redshifts z > 1.5 where major assembly is in progress. The search for galaxy clusters at high redshift, so far, has been mildly successful and only a handful of clusters at z > 1.5 have been confirmed. Because this redshift range was essentially unreachable with previous instrumentation, it was dubbed a ‘redshift desert’. The work presented in this thesis has made a major contribution to this field. The Clusters Around Radio- Loud AGN (CARLA) survey, a 400 hr targeted Warm Spitzer program, observed 420 radio-loud AGN (active galactic nuclei) at 1.3 < z < 3.2 across the full sky. Extensive literature over several decades shows that powerful radio-loud AGN preferentially reside in overdense environments. From this survey, we have identified a sample of ∼ 200 galaxy cluster candidates by selecting strong overdensities of color-selected sources. By studying the luminosity function of the CARLA cluster candidates, we showed that quenching is happening much earlier in clusters around radio-loud AGN than in field galaxy samples. This suggests that our targets may well be the most massive and evolved structures known to date at z > 1.5. We also showed that radio-loud AGN reside in denser environments than similarly massive galaxies. This makes high-redshift clusters around radio-loud AGN particularly interesting as they can reveal how galaxies in the most massive dark matter halos assembled. A complementary project, HERGE (Herschel Radio Galaxy Evolution Project) observed a sample of 71 radio galaxies at 1 < z < 5 at far-IR wavelengths with the Herschel Space Observatory. Supporting data in the mid-IR, partially in the near-IR and at sub-mm wave- lengths allow to study cluster fields in more detail. A pilot project on a single field showed that we can identify cluster members and constrain their star-formation properties. These projects laid the foundation for future work, which will make a significant impact on understanding the formation of the most massive structures over several billion years.

In dieser Promotionsarbeit präsentiere ich die erstmalige Realisierung eines Zustands negativer absoluter Temperatur für bewegliche Teilchen, sowie zusätzlich die detaillierte Untersuchung der Dynamik eines Quantenphasenübergangs. Als Grundlage für die Experimente dienten uns ultrakalte Atome in optischen Gittern, die durch den Bose-Hubbard Hamilton-Operator beschrieben werden können. Das Charakteristikum negativer Temperaturen ist eine invertierte Besetzungsverteilung, bei der Zustände hoher Energien stärker besetzt sind als niederenergetische Zustände. Daraus folgt die experimentelle Herausforderung, dass die möglichen Energien des Systems nach oben beschränkt sein müssen. Zum ersten Mal wurden negative Temperaturen in den 1950er Jahren in Bezug auf den Spinfreiheitsgrad von Atomkernen erreicht, welcher ein endliches Spektrum bildet. In dieser Arbeit stelle ich die erstmalige Realisierung von negativen Temperaturen auch für kinetische Freiheitsgrade vor. Dafür beschränkten wir die kinetische Energie auf ein einzelnes Band des Gitterpotenzials und nutzten die volle Flexibilität unseres Experiments, bestehend aus rotverstimmten Dipolfallen, blauverstimmten Gitterpotenzialen und einer Feshbach-Resonanz, um die Gesamtenergie des Systems zu limitieren. Durch die Messung der Impulsverteilung konnten wir nachweisen, dass die Atome vor allem Zustände höchster kinetischer Energie besetzen. Das Experiment ermöglicht in Zukunft unter anderem die Untersuchung von Systemen, bei denen der oberste Energiezustand besonders interessante Eigenschaften aufweist. In einem weiteren Experiment untersuchten wir das komplexe dynamische Verhalten an einem Quantenphasenübergang, das auch in der modernen Physik noch nicht vollständig verstanden ist. Quantenphasenübergänge zeichnen sich durch eine fundamentale Änderung von Grundzustandseigenschaften bei Variation eines Parameters aus; Beispiele sind das Auftreten von magnetischer Ordnung oder von Supraleitung als Funktion der Dotierung in Cupraten. In diesem Projekt untersuchten wir den Phasenübergang von Mott-Isolator zu Suprafluid, einen paradigmatischen Vertreter der Quantenphasenübergange, und dabei insbesondere, wie sich Kohärenz beim Übergang vom inkohärenten Mott-Isolator zum phasenkohärenten Suprafluid dynamisch aufbaut. Das komplexe Verhalten, das wir beobachten konnten, geht über die Vorhersagen existierender analytischer Modelle wie des Kibble-Zurek-Mechanismus' hinaus. Numerische Simulationen eindimensionaler Systeme unserer Kollegen von der FU Berlin stimmen hervorragend mit unseren experimentellen Daten überein und bestätigen unsere Messungen als zertifizierte Quantensimulation. Unsere umfangreichen Ergebnisse für unterschiedliche repulsive und attraktive Wechselwirkungen sowie Dimensionalitäten sind ein entscheidender Baustein, um in Zukunft ein tiefergehendes Verständnis des komplizierten dynamischen Verhaltens an Quantenphasenübergängen zu erreichen. / In this thesis, I present the first realization of negative absolute temperatures for mobile particles as well as a detailed study of the complex dynamics of a quantum phase transition, namely from the Mott insulator to the superfluid. The experiments are carried out with ultracold bosons loaded into an optical lattice, which can be described by the Bose-Hubbard Hamiltonian. The measurements presented in this thesis were only possible due to the extraordinary control over quantum states that can nowadays be achieved in modern ultracold atoms setups. Negative temperature states are characterized by an inverted occupation distribution, where high-energy states are populated more than low-energy states. This requires, as an experimental challenge, an upper bound on the possible energies of the system. Negative temperatures have been realized for the first time in the 1950s for the spin degree of freedom of nuclei, where the spectrum is finite. In this thesis, I present the first realization of negative temperatures for motional degrees of freedom. We limited the kinetic energy to a single band of the optical lattice potential and fully employed the tunability of our setup, including the combination of dipole potentials at blue- and red-detuned wavelengths and a Feshbach resonance, to create an upper bound on the total energy of the system. We identified the negative temperature state via its momentum distribution, which shows very strong occupation of the highest kinetic energy states. Amongst others, negative temperature states in optical lattices allow future research on systems where the highest energy state is of particular interest. In a separate set of experiments, we investigated the complex dynamical behavior when a quantum phase transition is crossed, which poses still an open and challenging question for many-body theory. Quantum phase transitions are characterized by a dramatic change of ground state properties, for example the appearance of magnetic order or superconductivity as a function of doping in cuprates. In this project, we investigated the Mott insulator to superfluid transition, a paradigmatic example of a quantum phase transition. We performed a detailed study on how coherence emerges when the quantum phase transition from the incoherent Mott insulator to the phase-coherent superfluid state is crossed and found a rich behavior beyond the scope of any existing analytical model such as the Kibble-Zurek mechanism. We obtained excellent agreement with the numerical simulations of one-dimensional systems of our collaborators, supporting that our measurements can be considered a valid quantum simulation. Our extensive results for various repulsive and attractive interactions as well as dimensionalities contribute an essential piece for a future comprehensive understanding of the intricate dynamics of quantum phase transitions.

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