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.

Effect of mixing, particle interaction, and spatial dimension on the glass transition

In this thesis, the influence of composition changes on the glass transition behavior of binary liquids in two and three spatial dimensions (2D/3D) is studied in the framework of mode-coupling theory (MCT).The well-established MCT equations are generalized to isotropic and homogeneous multicomponent liquids in arbitrary spatial dimensions. Furthermore, a new method is introduced which allows a fast and precise determination of special properties of glass transition lines. The new equations are then applied to the following model systems: binary mixtures of hard disks/spheres in 2D/3D, binary mixtures of dipolar point particles in 2D, and binary mixtures of dipolar hard disks in 2D. Some general features of the glass transition lines are also discussed. The direct comparison of the binary hard disk/sphere models in 2D/3D shows similar qualitative behavior. Particularly, for binary mixtures of hard disks in 2D the same four so-called mixing effects are identified as have been found before by Götze and Voigtmann for binary hard spheres in 3D [Phys. Rev. E 67, 021502 (2003)]. For instance, depending on the size disparity, adding a second component to a one-component liquid may lead to a stabilization of either the liquid or the glassy state. The MCT results for the 2D system are on a qualitative level in agreement with available computer simulation data. Furthermore, the glass transition diagram found for binary hard disks in 2D strongly resembles the corresponding random close packing diagram. Concerning dipolar systems, it is demonstrated that the experimental system of König et al. [Eur. Phys. J. E 18, 287 (2005)] is well described by binary point dipoles in 2D through a comparison between the experimental partial structure factors and those from computer simulations. For such mixtures of point particles it is demonstrated that MCT predicts always a plasticization effect, i.e. a stabilization of the liquid state due to mixing, in contrast to binary hard disks in 2D or binary hard spheres in 3D. It is demonstrated that the predicted plasticization effect is in qualitative agreement with experimental results. Finally, a glass transition diagram for binary mixtures of dipolar hard disks in 2D is calculated. These results demonstrate that at higher packing fractions there is a competition between the mixing effects occurring for binary hard disks in 2D and those for binary point dipoles in 2D.

Effects of low-density lipoprotein receptor-related protein 4 and apolipoprotein E isoforms on bone metabolism in vivo

LRP4, member of the LDLR family, is a multifunctional membrane-bound receptor that is expressed in various tissues. The expression of LRP4 by osteoblasts, its novel interaction with Wnt-signaling inhibitors Dkk1 and SOST, and the lower levels of activated beta-catenin in different bone locations described here, adds another player to the long list of established factors that modulate canonical Wnt-signaling in bone. By demonstrating that in addition to Wise, LRP4 is able to interact with two additional important modulators of Wnt- and BMP-signaling, our perspective of the complexity of the integration of BMP and Wnt-signaling pathways on the osteoblast surface has expanded further. Nevertheless the recently described association of both the SOST and LRP4 genes with BMD in humans, together with our findings suggest that LRP4 plays a physiologically important role in the skeletal development and bone metabolism not only in rodents, but in humans as well. The efficiency with which LRP4 binds both SOST and Dkk1, presumably at the osteoblastic surface, LRP4 may act as a sink and competes with LRP5/6 for the binding of these Wnt antagonists, which then are no longer available for suppression of the signal through the LRP5/6 axis. rnApoE, a 299 amino acid glycoprotein, is a crucial regulator in the uptake of triglyceride, phospholipids, cholesteryl esters, and cholesterol into cells. ApoE has been linked to osteoporosis, and such a role is further strengthened by the present of a high bone mass phenotype in ApoE null mice. Until recently, the effects of respective ApoE isoforms E2, E3, and E4, and their impact on bone metabolism, have been unclear. Here we report that respective human ApoE knockin mice display diverse effects on bone metabolism. ApoE2 mice show decreased trabecular bone volume per total volume in femoral bone and lumbar spine in comparison to ApoE3 and E4 animals. In this context, urinary bone resorption marker DPD is increased in these animals, which is accompanied by a low ratio of osteoclastogenesis markers OPG/RANKL. Interestingly, serum bone formation markers ALP and OCN are diminished in ApoE4 mice. In contrast to this finding, ApoE2 mice show the lowest bone formation of all groups in vivo. These findings cannot be explained by the low receptor-affinity of ApoE2 and subsequent decreased uptake of triglyceride-rich lipoproteins by osteoblasts, resulting in elevated levels of undercarboxylated osteocalcin. Thus, other crucial pathways relevant for bone metabolism, e. g. Wnt/beta-catenin-signaling pathways, must be, compared to the ApoE3/4 isoforms, more affected by the ApoE2 isoform.

Cannabinoid CB1 receptor in the regulation of sociability, stress coping, and its interaction with the serotonergic system

Cannabinerge Substanzen können das Verhalten in einer dosisabhängigen, aber biphasischen Weise beeinflussen. Eine Erklärung für diese Art der Effekte könnte die Verteilung des CB1 Rezeptors auf verschiedenen Neuronentypen sein. CB1 Rezeptoren in glutamatergen und GABAergen Neuronen sind hier besonders wichtig, da die entsprechenden Neurotransmitter als Gegenspieler die neuronale Erregung kontrollieren. Spezifische Deletion des CB1 Rezeptor-Gens von einer der beiden Populationen führte zu gegensätzlichen Phenotypen, genauer gesagt, einem erniedrigten, bzw. einem gesteigerten Interaktiondrang. Tiere, bei denen der CB1 Rezeptor ausschließlich in striatalen, GABAergen „Medium Spiny“ Neuronen deletiert wurde, zeigten keinen veränderten Phänotyp. Dies legt nahe, dass der CB1 Rezeptor in kortikalen glutamatergen und GABAergen Neuronen für einen ausgeglichenen Interaktionsdrang entscheidend ist (siehe Kapitel 3).rnDiese dosisabhängigen, biphasischen Effekte auf das Verhalten können auch im „Forced Swim Test“ (FST) beobachtet werden. Ein möglicher Mechanismus, durch den Cannabinoide das Stressverhalten beeinflussen können, wäre die Regulierung der Monoaminausschüttung. Um die Abhängigkeit der Cannabinoideffekte von der Serotonintransmission zu untersuchen, wurden Dosen von CB1 Rezeptoragonisten und –antagonisten mit antidepressiv-induzierenden Eigenschaften bei gleichzeitiger Inhibition der Serotonintransmission im FST getestet. Die Ergebnisse zeigten, dass lediglich der Agonisteffekt durch die Inhibition der Serotoninauschüttung beeinflusst wird. Zusätzlich konnte die Abhängigkeit des Antagonisteneffekts von funktionsfähigen GABAergen CB1 Rezeptoren nachweisen werden. Interessanter Weise konnte der durch die Deletion von glutamatergen CB1 Rezeptoren induzierte Phänotyp durch Inhibition der Serotoninausschüttung blockiert werden (siehe Kapitel 4).rnEin indirekter Einfluss auf Serotoninausschüttung scheint also wahrscheinlich zu sein. Bis jetzt blieb jedoch unklar, inwieweit cannabinerge Substanzen direkt auf serotonerge Neuronen wirken können. Im Jahr 2007 konnte unsere Gruppe die Expression des CB1 Rezeptors in serotonergen Neuronen auf mRNA- und Proteinebene nachweisen. Die Züchtung und Analyse einer mutanten Mauslinie, in welcher der CB1-Rezeptor spezifisch in serotonergen Neuronen ausgeschaltet wurde, zeigte bei männlichen Tieren eine schwache, aber signifikante Verhaltensänderungen, die durch soziale Stimuli und lebensbedrohlichen Situationen ausgelöst wurde. So ist es erstmals gelungen nachzuweisen, dass serotonerge CB1-Rezeptoren eine physiologische Relevanz besitzen (siehe Kapitel 5).rn