Interacting fermionic atoms in optical lattices - A quantum simulator for condensed matter physics

This thesis reports on the creation and analysis of many-body states of interacting fermionic atoms in optical lattices. The realized system can be described by the Fermi-Hubbard hamiltonian, which is an important model for correlated electrons in modern condensed matter physics. In this way, ultra-cold atoms can be utilized as a quantum simulator to study solid state phenomena. The use of a Feshbach resonance in combination with a blue-detuned optical lattice and a red-detuned dipole trap enables an independent control over all relevant parameters in the many-body hamiltonian. By measuring the in-situ density distribution and doublon fraction it has been possible to identify both metallic and insulating phases in the repulsive Hubbard model, including the experimental observation of the fermionic Mott insulator. In the attractive case, the appearance of strong correlations has been detected via an anomalous expansion of the cloud that is caused by the formation of non-condensed pairs. By monitoring the in-situ density distribution of initially localized atoms during the free expansion in a homogeneous optical lattice, a strong influence of interactions on the out-of-equilibrium dynamics within the Hubbard model has been found. The reported experiments pave the way for future studies on magnetic order and fermionic superfluidity in a clean and well-controlled experimental system.

Interacting bosons and fermions in three-dimensional optical lattice potentials

This thesis reports on the realization, characterization and analysis of ultracold bosonic and fermionic atoms in three-dimensional optical lattice potentials. Ultracold quantum gases in optical lattices can be regarded as ideal model systems to investigate quantum many-body physics. In this work interacting ensembles of bosonic 87Rb and fermionic 40K atoms are employed to study equilibrium phases and nonequilibrium dynamics. The investigations are enabled by a versatile experimental setup, whose core feature is a blue-detuned optical lattice that is combined with Feshbach resonances and a red-detuned dipole trap to allow for independent control of tunneling, interactions and external confinement. The Fermi-Hubbard model, which plays a central role in the theoretical description of strongly correlated electrons, is experimentally realized by loading interacting fermionic spin mixtures into the optical lattice. Using phase-contrast imaging the in-situ size of the atomic density distribution is measured, which allows to extract the global compressibility of the many-body state as a function of interaction and external confinement. Thereby, metallic and insulating phases are clearly identified. At strongly repulsive interaction, a vanishing compressibility and suppression of doubly occupied lattice sites signal the emergence of a fermionic Mott insulator. In a second series of experiments interaction effects in bosonic lattice quantum gases are analyzed. Typically, interactions between microscopic particles are described as two-body interactions. As such they are also contained in the single-band Bose-Hubbard model. However, our measurements demonstrate the presence of multi-body interactions that effectively emerge via virtual transitions of atoms to higher lattice bands. These findings are enabled by the development of a novel atom optical measurement technique: In quantum phase revival spectroscopy periodic collapse and revival dynamics of the bosonic matter wave field are induced. The frequencies of the dynamics are directly related to the on-site interaction energies of atomic Fock states and can be read out with high precision. The third part of this work deals with mixtures of bosons and fermions in optical lattices, in which the interspecies interactions are accurately controlled by means of a Feshbach resonance. Studies of the equilibrium phases show that the bosonic superfluid to Mott insulator transition is shifted towards lower lattice depths when bosons and fermions interact attractively. This observation is further analyzed by applying quantum phase revival spectroscopy to few-body systems consisting of a single fermion and a coherent bosonic field on individual lattice sites. In addition to the direct measurement of Bose-Fermi interaction energies, Bose-Bose interactions are proven to be modified by the presence of a fermion. This renormalization of bosonic interaction energies can explain the shift of the Mott insulator transition. The experiments of this thesis lay important foundations for future studies of quantum magnetism with fermionic spin mixtures as well as for the realization of complex quantum phases with Bose-Fermi mixtures. They furthermore point towards physics that reaches beyond the single-band Hubbard model.

Surface-functionalized latex particles as additives in the mineralization of zinc oxide

Polystyrene latex particles modified at the surface with different hydrophilic functional groups were prepared by miniemulsion polymerization and applied to control the crystallization of zinc oxide in aqueous medium. The effects of both latex structure and concentration on the crystal growth, morphology, crystalline structure, and properties of the resulting zinc oxide were analyzed. Depending on the latex additive used, micro- and submicrosized crystals with a broad variety of morphologies were obtained. Among the studied latexes, the carboxyl-derived particles were shown to be a convenient system for further quantitative investigations. In this case, as the additive concentration increases, the aspect ratio of the crystals decreases systematically. Latex particles are assumed to adsorb preferentially onto the fast growing {001} faces of ZnO, interacting with the growth centers and reducing the growth rate in [001]. When zinc oxide is precipitated in the presence of latex, the polymer particles become incorporated into the growing crystals and polymer–inorganic hybrid materials are obtained. These materials are composed of an inorganic and largely undisturbed crystalline matrix in which organic latex particles are embedded. Increasing amounts of latex become incorporated into the growing crystals at increasing overall concentration in the crystallizing system. Photoluminescence (PL) spectra were measured to obtain information on defect centers. Emission spectra of all samples showed a narrow UV peak and a broad band in the green-yellow spectral region. The former emission is attributed to exciton recombination, whereas the latter seems to be related with deep-level donors. Latex appears to be a quencher of the visible emission of zinc oxide. Thus, compared to pure zincite, ZnO–latex hybrid materials show a significantly lower PL intensity in the visible range of the spectrum. Under continuous photoexcitation, a noticeable dynamic behavior of the PL is observed, which can be related to a photodesorption of adsorbed oxygen. These surface-adsorbed oxygen species seem to play a crucial role for the optical properties of the materials and may mediate the tunneling of electrons from the conduction band to preexisting deep-level traps, probably related to intrinsic defects (oxygen vacancies or interstitial zinc). The polymer particles can block the sites where oxygen adsorbs, and the disappearance of the “electron-shuttle” species leads to the observed quenching of the visible emission. Electron paramagnetic resonance (EPR) provided additional information about crystal defects with unpaired electrons. Spectra of all samples exhibit a single signal at g ≈ 1.96, typical for shallow donors. Contrary to the results of other authors, no correlation was possible between the EPR signal and the visible range of PL spectra, which suggests that centers responsible for the visible emission and the EPR signal are different.

Interacting Bose-Fermi mixtures in optical lattices

In this thesis, we investigate mixtures of quantum degenerate Bose and Fermi gases of neutral atoms in threedimensional optical lattices. Feshbach resonances allow to control interspecies interactions in these systems precisely, by preparing suitable combinations of internal atomic states and applying external magnetic fields. This way, the system behaviour can be tuned continuously from mutual transparency to strongly interacting correlated phases, up to the stability boundary.rnThe starting point for these investigations is the spin-polarized fermionic band insulator. The properties of this non-interacting system are fully determined by the Pauli exclusion principle for the occupation of states in the lattice. A striking demonstration of the latter can be found in the antibunching of the density-density correlation of atoms released from the lattice. If bosonic atoms are added to this system, isolated heteronuclear molecules can be formed on the lattice sites via radio-frequency stimulation. The efficiency of this process hints at a modification of the atom number distribution over the lattice caused by interspecies interaction.rnIn the following, we investigate systems with tunable interspecies interaction. To this end, a method is developed which allows to assess the various contributions to the system Hamiltonian both qualitatively and quantitatively by following the quantum phase diffusion of the bosonic matter wave.rnBesides a modification of occupation number statistics, these measurements show a significant renormalization of the bosonic Hubbard parameters. The final part of the thesis considers the implications of this renormalization effect on the many particle physics in the mixture. Here, we demonstrate how the quantum phase transition from a bosonic superfluid to a Mott insulator state is shifted towards considerably shallower lattices due to renormalization.

Interacting quantum-dissipative tunnelling systems

Die Untersuchung von dissipativen Quantensystemen erm¨oglicht es, Quantenph¨anomene auch auf makroskopischen L¨angenskalen zu beobachten. Das in dieser Dissertation gew¨ahlte mikroskopische Modell erlaubt es, den bisher nur ph¨anomenologisch zug¨anglichen Effekt der Quantendissipation mathematisch und physikalisch herzuleiten und zu untersuchen. Bei dem betrachteten mikroskopischen Modell handelt es sich um eine 1-dimensionale Kette von harmonischen Freiheitsgraden, die sowohl untereinander als auch an r anharmonische Freiheitsgrade gekoppelt sind. Die F¨alle einer, respektive zwei anharmonischer Bindungen werden in dieser Arbeit explizit betrachtet. Hierf¨ur wird eine analytische Trennung der harmonischen von den anharmonischen Freiheitsgraden auf zwei verschiedenen Wegen durchgef¨uhrt. Das anharmonische Potential wird als symmetrisches Doppelmuldenpotential gew¨ahlt, welches mit Hilfe der Wick Rotation die Berechnung der ¨Uberg¨ange zwischen beiden Minima erlaubt. Das Eliminieren der harmonischen Freiheitsgrade erfolgt mit Hilfe des wohlbekannten Feynman-Vernon Pfadintegral-Formalismus [21]. In dieser Arbeit wird zuerst die Positionsabh¨angigkeit einer anharmonischen Bindung im Tunnelverhalten untersucht. F¨ur den Fall einer fernab von den R¨andern lokalisierten anharmonischen Bindung wird ein Ohmsches dissipatives Tunneln gefunden, was bei der Temperatur T = 0 zu einem Phasen¨ubergang in Abh¨angigkeit einer kritischen Kopplungskonstanten Ccrit f¨uhrt. Dieser Phasen¨ubergang wurde bereits in rein ph¨anomenologisches Modellen mit Ohmscher Dissipation durch das Abbilden des Systems auf das Ising-Modell [26] erkl¨art. Wenn die anharmonische Bindung jedoch an einem der R¨ander der makroskopisch grossen Kette liegt, tritt nach einer vom Abstand der beiden anharmonischen Bindungen abh¨angigen Zeit tD ein ¨Ubergang von Ohmscher zu super- Ohmscher Dissipation auf, welche im Kern KM(τ ) klar sichtbar ist. F¨ur zwei anharmonische Bindungen spielt deren indirekteWechselwirkung eine entscheidende Rolle. Es wird gezeigt, dass der Abstand D beider Bindungen und die Wahl des Anfangs- und Endzustandes die Dissipation bestimmt. Unter der Annahme, dass beide anharmonischen Bindung gleichzeitig tunneln, wird eine Tunnelwahrscheinlichkeit p(t) analog zu [14], jedoch f¨ur zwei anharmonische Bindungen, berechnet. Als Resultat erhalten wir entweder Ohmsche Dissipation f¨ur den Fall, dass beide anharmonischen Bindungen ihre Gesamtl¨ange ¨andern, oder super-Ohmsche Dissipation, wenn beide anharmonischen Bindungen durch das Tunneln ihre Gesamtl¨ange nicht ¨andern.

Bio-inspired polymer-supported nitrido molybdenum(VI) complexes for ammonia synthesis − reactivity towards protons and electrons : EPR investigations on paramagnetic molybdenum(V) and copper(II) complexes

Die biologische Stickstofffixierung durch Molybdän-haltige Nitrogenasen sowie die Erforschung des zugrundeliegenden komplexen Mechanismus (N2-Aktivierung an Metall-Zentren, 6-fache Protonierung und Reduktion, N–N Bindungsspaltung unter Bildung von Ammoniak) ist von erheblichem Interesse. Insbesondere Molybdän-Komplexe wurden bereits erfolgreich als Modellverbindungen für die Untersuchung elementarer Einzelschritte der N2-Aktivierung eingesetzt. Durch die Verwendung von Triamidoamin-Liganden ist es Schrock et al. sogar gelungen mehrere Katalysezyklen zu durchlaufen und einen Mechanismus zu formulieren. Trotz der sterisch anspruchsvollen Substituenten in den Schrock-Komplexen ist die Umsatzrate dieses homogenen Katalysators, aufgrund Komplex-Deaktivierung infolge intermolekularer Reaktionen wie Dimerisierung und Disproportionierung, limitiert. In der vorliegenden Arbeit wurden einige dieser Herausforderungen angegangen und die aktiven Spezies auf einer Festphase immobilisiert, um intermolekulare Reaktionen durch räumliche Isolierung der Komplexe zu unterdrücken.rnEin Polymer-verankertes Analogon des Schrock Nitrido-Molybdän(VI)-Komplexes wurde auf einem neuen Reaktionsweg synthetisiert. Dieser beinhaltet nur einen einzigen Reaktionsschritt, um die funktionelle Gruppe „MoN“ einzuführen. Protonierung des immobilisierten Nitrido-Molybdän(VI)-Komplexes LMoVIN (L = Polymer-verankerter Triamidoamin-Ligand) mit 2,6-Lutidinium liefert den entsprechenden Imido-Molybdän(VI)-Komplex. Durch anschließende Ein-Elektronen-Reduktion mit Cobaltocen wird der Polymer-angebundene Imido-Molybdän(V)-Komplex erhalten, bewiesen durch EPR-Spektroskopie (g1,2,3 = 1.989, 1.929, 1.902). Durch die Immobilisierung und die effektive räumliche Separation der Reaktionszentren auf der Festphase werden bimolekulare Nebenreaktionen, die oft in homogenen Systemen auftreten, unterdrückt. Dies ermöglicht zum ersten Mal die Darstellung des Imido-Molybdän(V)-Intermediates des Schrock-Zyklus.rnEPR-Spektren des als Spin-Label eingeführten immobilisierten Nitrato-Kupfer(II)-Komplexes wurden unter verschiedenen Bedingungen (Lösungsmittel, Temperatur) aufgenommen, wobei sich eine starke Abhängigkeit zwischen der Zugänglichkeit und Reaktivität der immobilisierten Reaktionszentren und der Art des Lösungsmittels zeigte. Somit wurde die Reaktivität von LMoVIN gegenüber Protonen und Elektronen, welches zur Bildung von NH3 führt, unter Verwendung verschiedener Lösungsmittel untersucht und optimiert. Innerhalb des kugelförmigen Polymers verläuft die Protonierung und Reduktion von LMoVIN stufenweise. Aktive Zentren, die sich an der „äußeren Schale“ des Polymers befinden, sind gut zugänglich und reagieren schnell nach H+/e− Zugabe. Aktive Zentren im „Inneren des Polymers“ hingegen sind schlechter zugänglich und zeigen langsame diffusions-kontrollierte Reaktionen, wobei drei H+/e− Schritte gefolgt von einer Ligandenaustausch-Reaktion erforderlich sind, um NH3 freizusetzen: LMoVIN  LMoVNH  LMoIVNH2  LMoIIINH3 und anschließender Ligandenaustausch führt zur Freisetzung von NH3.rnIn einem weiteren Projekt wurde der Bis(ddpd)-Kupfer(II)-Komplex EPR-spektroskopisch in Hinblick auf Jahn−Teller-Verzerrung und -Dynamik untersucht. Dabei wurden die EPR-Spektren bei variabler Temperatur (70−293 K) aufgenommen. Im Festkörperspektrum bei T < 100 K erscheint der Kupfer(II)-Komplex als gestreckter Oktaeder, wohingegen das EPR-Spektrum bei höheren Temperaturen g-Werte aufzeigt, die einer pseudo-gestauchten oktaedrischen Kupfer(II)-Spezies zuzuordnen sind. Diese Tatsache wird einem intramolekularen dynamischen Jahn−Teller Phänomen zugeschrieben, welcher bei 100 K eingefroren wird.

Measurement of the ZZ production cross section and limits to the anomalous triple gauge couplings with forward electrons with the ATLAS detector

Measurements of the self coupling between bosons are important to test the electroweak sector of the Standard Model (SM). The production of pairs of Z bosons through the s-channel is forbidden in the SM. The presence of physics, beyond the SM, could lead to a deviation of the expected production cross section of pairs of Z bosons due to the so called anomalous Triple Gauge Couplings (aTGC). Proton-proton data collisions at the Large Hadron Collider (LHC) recorded by the ATLAS detector at a center of mass energy of 8 TeV were analyzed corresponding to an integrated luminosity of 20.3 fb-1. Pairs of Z bosons decaying into two electron-positron pairs are searched for in the data sample. The effect of the inclusion of detector regions corresponding to high values of the pseudorapidity was studied to enlarge the phase space available for the measurement of the ZZ production. The number of ZZ candidates was determined and the ZZ production cross section was measured to be: rn7.3±1.0(Stat.)±0.4(Sys.)±0.2(lumi.)pb, which is consistent with the SM expectation value of 7.2±0.3pb. Limits on the aTGCs were derived using the observed yield, which are twice as stringent as previous limits obtained by ATLAS at a center of mass energy of 7 TeV.