Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

This work describes experiments with quantum-degenerate atomic mixtures at ultracold temperatures, where quantum statistics determine macroscopic system properties. The first heteronuclear molecules at ultracold temperatures are formed in a quantum degenerate two-species Fermi-Fermi mixture on the repulsive side of a narrow s-wave Feshbach resonance. Elastic collisions in this mixture are investigated with the method of cross-dimensional relaxation. Long-lived two-body bound states on the atomic side of the resonance are detected due to a many-body effect at the crossover of the narrow Feshbach resonance. In addition, atom scattering with fermionic 40K on a light field grating in the Bragg and Kapitza-Dirac regimes is realized for the first time.

The versatile experimental platform, where the investigations are done, offers the possibility to perform studies on mixtures involving the bosonic species 87Rb and the two fermionic species 6Li and 40K. Within this work, mainly interactions between the two fermionic species are considered. A quantum-degenerate mixture of 6Li and 40K can be used to create heteronuclear bosonic molecules close to an interspecies s-wave Feshbach resonance. By an adiabatic magnetic field sweep, up to 4 × 10^4 molecules are produced

with conversion efficiencies close to 50%. A direct and sensitive molecule detection method is developed to probe molecule properties. The lifetime of the molecules in an

atom-molecule mixture exhibits a strong magnetic field dependence. Close to resonance, lifetimes of more than 100ms are observed what offers excellent starting conditions for further investigation and manipulation of the molecular cloud.

The interspecies Feshbach resonance, which serves for the production of molecules, is further characterized. The method of cross-dimensional relaxation is applied for the

first time to a Fermi-Fermi mixture. For this method, a non-equilibrium state is created, which rethermalizes by pure interspecies collisions due to the fermionic nature of the two species. The lighter atomic species, 6Li, relaxes faster in the mixture than the heavier one, 40K. This is verified by an analytical model, Monte-Carlo simulations, and measurements. With this technique, elastic scattering cross sections are measured over a wide range of magnetic field strengths across the Feshbach resonance. The position (B0 = 154.71(5)G) and the magnetic field width of the Feshbach resonance (Delta = 1.02(7)G) are determined.

By comparison of the several measurements, long-lived bound states exist on the atomic side of the resonance due to a many-body effect in the crossover regime of the resonance.

In addition, atomic scattering with ultracold 40K on a light field crystal is studied for the first time. The light grating is generated by two counter-propagating laser beams. Suitable pulse parameters for the realization of atom scattering in the Bragg and Kapitza-Dirac regime are found. The momentum spread of the cloud determines the efficiency of the scattering process, which is increased by lowering the temperature of the system.

Um Galaxien, Galaxienhaufen oder noch größere Strukturen im

Universum detailliert zu simulieren, benötigt man eine korrekte Simulation des in diesen Objekten vorhandenen Gases. Eine Möglichkeit zur Simulation dieses Gases bietet

das etablierte Verfahren ``Smoothed Particle Hydrodynamics (SPH)''. Diese Methode empfiehlt sich besonders wegen ihrer intrinsischen geometrischen Flexibilität und ihrer adaptiven Auflösung. Neuere Untersuchungen zeigten aber, dass SPH in Situationen, in denen große Dichtesprünge auftreten, ungenau wird. Hier kann es zu einem unphysikalisch verlangsamten Wachstum von hydrodynamischen Instabilitäten kommen. Diese Probleme von SPH können vor allem auf systematisch bedingte Ungenauigkeiten in der Dichtebestimmung dieser Methode zurückgeführt werden. Um diese Probleme zu vermeiden, haben wir eine neue ``Voronoi Particle Hydrodynamics'' (VPH) genannte Methode enwickelt, um die Hydrodynamik zu simulieren. Dabei wird die Dichte der Simulationsteilchen mit Hilfe eines zusätzlichen Gitters bestimmt. Dieses Gitter ist eine Voronoi Pflasterung, die auf auf den Positionen der Teilchen basiert. Mit Hilfe dieses Prinzips können hydrodynamische

Instabilitäten korrekt simuliert werden. Situationen, in denen Scherströmungen entlang großer Dichtesprünge auftreten und zu hydrodynamische Instabilitäten führen,

sind besonders ungünstig für SPH, da es hier zu großen Ungenauigkeiten kommen kann. Eine Anwendung, in der

solche Situationen zu erwarten sind, ist der Einfall einer Galaxie in einen Galaxienhaufen. Dabei verliert die Galaxie aufgrund des anströmenden Galaxienhaufen-Gases zunehmend Gas an den Galaxienhaufen. Da SPH aufgrund seiner

Dichtebestimmung diesen Prozess nicht korrekt simuliert, ermittelt SPH einen zu geringen Verlust von Gas. Wir konnten dies mit Hilfe unserer Simulationen belegen.

Wir haben diese Resultate sowohl mit Simulationen von Galaxien, die in einen Galaxienhaufen fallen, als auch mit

kosmologischen Simulationen von sich bildenden Galaxienhaufen überprüft. Dort bestätigte sich, dass in SPH der Gasverlust der einfallenen Galaxien zu gering ist. Desweiteren ist der Gasverlust in den AREPO Simulationen stets am höchsten, während VPH eine mittlere Stellung einnimmt. Wir konnten ingesamt zeigen, dass VPH in

Situationen mit großem Dichtekontrast eine Verbesserung zu SPH darstellt. Auch wenn unsere Resultate keine vollständige Übereinstimmung mit dem Gitter-basierten

AREPO Code zeigen, stellen sie doch eine wichtige Annährung

zwischen Teilchen- und Gitter-basierten hydrodynamischen Verfahren dar. VPH empfiehlt sich vor allem als eine gegenüber SPH verbesserte Methode zur Simulation von hydrodynamischen Prozesssen in kosmologischen Problemen.

This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice.

We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism.

In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study

one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing

scheme leaves most atoms in the vibrational ground state.

Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available.

The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.

Dwarf galaxies are related to important cosmological questions, and central to our understanding of the physics of galaxy formation. In this thesis, I present the results of cosmological, hydrodynamical simulations of the formation and evolution of dwarf galaxies. I compare the simulation results with observations, and interpret them

in the context of a Lambda-CDM cosmology.

In high resolution simulations of isolated dwarf galaxies, I show that a combination of supernova feedback and the cosmic UV background results in the formation of galaxies with properties similar to the Local Group dwarf spheroidals, and that both effects are strongly moderated by the depth of the gravitational potential. The simulations

naturally reproduce the observed scaling relations between luminosity and mass-to-light ratio, and between total stellar mass and metallicities. The final objects have halo masses between 2.3 x 10^8 and 1.1 x 10^9 solar masses, mean velocity dispersions between 6.5 and 9.7 kms^-1, stellar masses ranging from 5 x 10^5 to 1.2 x 10^7 solar masses, median metallicities between [Fe/H]=-1.8 and -1.1, and half-light radii of the order of 200 to 300 pc, all comparable with Local Group dwarf spheroidals. The simulations also indicate that the dwarf spheroidal galaxies observed today lie near a mass threshold around 10^9 solar masses, in agreement with stellar kinematic data, where supernova feedback not only suffices to completely expel the interstellar medium and leave the residual gas-free, but where the combination of feedback, UV radiation and self-shielding establishes a dichotomy of age distributions similar to that observed in the Milky Way and M31 satellites.

A second line of work has been the analysis of the dwarf galaxy population resulting from the Aquila simulation. By simultaneously including the formation of a Milky Way type galaxy along with ~500 dwarf-sized haloes in the mass range of ~10^8 - 10^10 solar masses, this simulation allows a study of the effect of the environment on dwarf galaxy evolution. I study the relative importance, and interplay, of the different mechanisms for gas loss, and compare the properties of the satellites with those of isolated dwarf galaxies.

A third set of simulations focuses on the formation of dwarf galaxies in a representative sample of haloes extracted from the Millennium-II simulation. The six haloes in these simulations all have a z=0 mass of ~10^10 solar masses and show different mass assembly histories, which are reflected in different star formation histories. The galaxies reach final stellar masses in the range of 5 x 10^7 - 10^8 solar masses, consistent with other published simulations of galaxy formation in similar mass haloes. The resulting objects have structures and stellar populations consistent with dwarf elliptical and dwarf irregular galaxies. However, in a Lambda-CDM universe, 10^10 solar mass haloes must typically contain galaxies with much lower stellar mass than these simulations predict, if they are to match observed galaxy abundances. The dwarf galaxies formed in my own and all other current hydrodynamical simulations are more than an order of magnitude more luminous than expected for haloes of this mass. I discuss the significance and possible implications of this result for cosmological models, and for the assumptions about the physics of galaxy formation.

Finally, I present preliminary results of a direct comparison between hydrodynamical simulations and semi-analytical models for the formation of dwarf galaxies. Current semi-analytical models, which are tuned to match the statistical properties of galaxies, do not agree with the predictions of hydrodynamical simulations for individual

objects. Conversely, when tuned to accurately reproduce the

simulations, semi-analytical models can give a more qualitative interpretation of the simulation results, in terms of equations of galaxy formation. The combination of the two methods allows an extrap

This thesis reports on theoretical and experimental examination of two-photon direct frequency comb spectroscopy (DFCS) using atomic two-level systems.

This method is a very promising tool to extend optical spectroscopy into the short wavelength region where only few cw laser sources exist. The high peak intensities of pulsed lasers facilitate efficient nonlinear conversion into frequency regions which are so far unexplored, for example by high harmonic generation (HHG). DFCS is based on theoretical work in the 1970s which showed that a pulse train of a mode-locked laser drives a two-photon transition as efficient as a cw laser of same average power. Thereby the effective line width is determined by the narrow width of a single comb mode rather than by the spectral width of a single pulse. In this way a frequency comb combines the spectral purity of a cw laser with the high peak intensity of a pulsed laser.

To demonstrate the capability of a nonlinearly converted frequency comb for DFCS, the absolute frequency of a two-photon transition in $^{24}$Mg at 431~nm was measured in a first experiment. The accuracies of the values could be improved by more than two orders of magnitude with respect to previously reported values.

Furthermore two crucial effects which affect the transition rates were analyzed quantitatively for the first time: the impact of a linear chirp and non-centered spectral envelope on the spectroscopy. In general the pulses of a nonlinear converted frequency comb are not bandwidth limited leading to a partially destructive pairwise addition of modes. To describe the impact of a linear chirp a theoretical model was developed and verified experimentally using two-photon spectroscopy on cesium. Moreover, theory and experiment have shown a Gaussian decrease in the transition rate with increasing detuning of the laser spectrum.

%Another important aspect is the centering of the laser spectrum with respect to the atomic transition. Theory and experiment show here a Gaussian decrease in the transition rate with increasing detuning.

Finally the progress of $1S - 3S$ spectroscopy in hydrogen is presented. This transition is a promising candidate for a test of bound state quantum electrodynamics. Using cw lasers the required wavelength of 205~nm is hard to generate, making this transition to an eligible system for DFCS. Beside the experimental achievements also the lessons learned from Cs and Mg spectroscopy and their consequences for the H spectroscopy are discussed.

In the scope of this work a frequency quadrupled laser system was extended and improved, providing ps frequency combs of high average power and good beam profile at 820~nm, 410~nm and 205~nm. An overall output power of max. 100~mW is now available at 205~nm, the up to date highest power generated by SHG. Moreover for H spectroscopy a new spectrometer was designed and built.