A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

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.

Probing strongly correlated states of ultracold atoms in optical lattices

This thesis describes experiments which investigate ultracold atom ensembles in an optical lattice. Such quantum gases are powerful models for solid state physics. Several novel methods are demonstrated that probe the special properties of strongly correlated states in lattice potentials. Of these, quantum noise spectroscopy reveals spatial correlations in such states, which are hidden when using the usual methods of probing atomic gases. Another spectroscopic technique makes it possible to demonstrate the existence of a shell structure of regions with constant densities. Such coexisting phases separated by sharp boundaries had been theoretically predicted for the Mott insulating state. The tunneling processes in the optical lattice in the strongly correlated regime are probed by preparing the ensemble in an optical superlattice potential. This allows the time-resolved observation of the tunneling dynamics, and makes it possible to directly identify correlated tunneling processes.

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 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.

NMR spectroscopy and imaging of hyperpolarized gases

Since the discovery of the nuclear magnetic resonance (NMR) phenomenon, countless NMR techniques have been developed that are today indispensable tools in physics, chemistry, biology, and medicine. As one of the main obstacles in NMR is its notorious lack of sensitivity, different hyperpolarization (HP) methods have been established to increase signals up to several orders of magnitude. In this work, different aspects of magnetic resonance, using HP noble gases, are studied, hereby combining different disciplines of research. The first part examines new fundamental effects in NMR of HP gases, in theory and experiment. The spin echo phenomenon, which provides the basis of numerous modern experiments, is studied in detail in the gas phase. The changes of the echo signal in terms of amplitude, shape, and position, due to the fast translational motion, are described by an extension of the existing theory and computer simulations. With this knowledge as a prerequisite, the detection of intermolecular double-quantum coherences was accomplished for the first time in the gas phase. The second part of this thesis focuses on the development of a practical method to enhance the dissolution process of HP 129Xe, without loss of polarization or shortening of T1. Two different setups for application in NMR spectroscopy and magnetic resonance imaging (MRI) are presented. The continuous operation allows biological and multidimensional spectroscopy in solutions. Also, first in vitro MRI images with dissolved HP 129Xe as contrast agent were obtained at a clinical scanner.

Diffusion of laser polarized gases in MRI

The use of Magnetic Resonance Imaging (MRI) as a diagnostic tool is increasingly employing functional contrast agents to study or contrast entire mechanisms. Contrast agents in MRI can be classified in two categories. One type of contrast agents alters the NMR signal of the protons in its surrounding, e.g. lowers the T1 relaxation time. The other type enhances the Nuclear Magnetic Resonance (NMR) signal of specific nuclei. For hyperpolarized gases the NMR signal is improved up to several orders of magnitude. However, gases have a high diffusivity which strongly influences the NMR signal strength, hence the resolution and appearance of the images. The most interesting question in spatially resolved experiments is of course the achievable resolution and contrast by controlling the diffusivity of the gas. The influence of such diffusive processes scales with the diffusion coefficient, the strength of the magnetic field gradients and the timings used in the experiment. Diffusion may not only limit the MRI resolution, but also distort the line shape of MR images for samples, which contain boundaries or diffusion barriers within the sampled space. In addition, due to the large polarization in gaseous 3He and 129Xe, spin diffusion (different from particle diffusion) could play a role in MRI experiments. It is demonstrated that for low temperatures some corrections to the NMR measured diffusion coefficient have to be done, which depend on quantum exchange effects for indistinguishable particles. Physically, if these effects can not change the spin current, they can do it indirectly by modifying the velocity distribution of the different spin states separately, so that the subsequent collisions between atoms and therefore the diffusion coefficient can eventually be affected. A detailed study of the hyperpolarized gas diffusion coefficient is presented, demonstrating the absence of spin diffusion (different from particle diffusion) influence in MRI at clinical conditions. A novel procedure is proposed to control the diffusion coefficient of gases in MRI by admixture of inert buffer gases. The experimental measured diffusion agrees with theoretical simulations. Therefore, the molecular mass and concentration enter as additional parameters into the equations that describe structural contrast. This allows for setting a structural threshold up to which structures contribute to the image. For MRI of the lung this allows for images of very small structural elements (alveoli) only, or in the other extreme, all airways can be displayed with minimal signal loss due to diffusion.

Bottle microresonators for applications in quantum optics and all-optical signal processing

This thesis reports on the experimental realization, characterization and application of a novel microresonator design. The so-called “bottle microresonator” sustains whispering-gallery modes in which light fields are confined near the surface of the micron-sized silica structure by continuous total internal reflection. While whispering-gallery mode resonators in general exhibit outstanding properties in terms of both temporal and spatial confinement of light fields, their monolithic design makes tuning of their resonance frequency difficult. This impedes their use, e.g., in cavity quantum electrodynamics (CQED) experiments, which investigate the interaction of single quantum mechanical emitters of predetermined resonance frequency with a cavity mode. In contrast, the highly prolate shape of the bottle microresonators gives rise to a customizable mode structure, enabling full tunability. The thesis is organized as follows: In chapter I, I give a brief overview of different types of optical microresonators. Important quantities, such as the quality factor Q and the mode volume V, which characterize the temporal and spatial confinement of the light field are introduced. In chapter II, a wave equation calculation of the modes of a bottle microresonator is presented. The intensity distribution of different bottle modes is derived and their mode volume is calculated. A brief description of light propagation in ultra-thin optical fibers, which are used to couple light into and out of bottle modes, is given as well. The chapter concludes with a presentation of the fabrication techniques of both structures. Chapter III presents experimental results on highly efficient, nearly lossless coupling of light into bottle modes as well as their spatial and spectral characterization. Ultra-high intrinsic quality factors exceeding 360 million as well as full tunability are demonstrated. In chapter IV, the bottle microresonator in add-drop configuration, i.e., with two ultra-thin fibers coupled to one bottle mode, is discussed. The highly efficient, nearly lossless coupling characteristics of each fiber combined with the resonator's high intrinsic quality factor, enable resonant power transfers between both fibers with efficiencies exceeding 90%. Moreover, the favorable ratio of absorption and the nonlinear refractive index of silica yields optical Kerr bistability at record low powers on the order of 50 µW. Combined with the add-drop configuration, this allows one to route optical signals between the outputs of both ultra-thin fibers, simply by varying the input power, thereby enabling applications in all-optical signal processing. Finally, in chapter V, I discuss the potential of the bottle microresonator for CQED experiments with single atoms. Its Q/V-ratio, which determines the ratio of the atom-cavity coupling rate to the dissipative rates of the subsystems, aligns with the values obtained for state-of-the-art CQED microresonators. In combination with its full tunability and the possibility of highly efficient light transfer to and from the bottle mode, this makes the bottle microresonator a unique tool for quantum optics applications.

Preparation of cold Mg + ion clouds for sympathetic cooling of highly charged ions at SPECTRAP

Die Elektronen in wasserstoff- und lithium-ähnlichen schweren Ionen sind den extrem starken elektrischen und magnetischen Feldern in der Umgebung des Kerns ausgesetzt. Die Laserspektroskopie der Hyperfeinaufspaltung im Grundzustand des Ions erlaubt daher einen sensitiven Test der Quantenelektrodynamik in starken Feldern insbesondere im magnetischen Sektor. Frühere Messungen an wasserstoffähnlichen Systemen die an einer Elektronenstrahl-Ionenfalle (EBIT) und am Experimentierspeicherring (ESR) der GSI Darmstadt durchgeführt wurden, waren in ihrer Genauigkeit durch zu geringe Statistik, einer starken Dopplerverbreiterung und der großen Unsicherheit in der Ionenenergie limitiert. Das ganze Potential des QED-Tests kann nur dann ausgeschöpft werden, wenn es gelingt sowohl wasserstoff- als auch lithium-ähnliche schwere Ionen mit einer um 2-3 Größenordnung gesteigerten Genauigkeit zu spektroskopieren. Um dies zu erreichen, wird gegenwärtig das neue Penningfallensystem SPECTRAP an der GSI aufgebaut und in Betrieb genommen. Es ist speziell für die Laserspektroskopie an gespeicherten hochgeladenen Ionen optimiert und wird in Zukunft von HITRAP mit nierderenergetischen hochgeladenen Ionen versorgt werden.rnrnSPECTRAP ist eine zylindrische Penningfalle mit axialem Zugang für die Injektion von Ionen und die Einkopplung eines Laserstrahls sowie einem radialen optischen Zugang für die Detektion der Fluoreszenz. Um letzteres zu realisieren ist der supraleitende Magnet als Helmholtz-Spulenpaar ausgelegt. Um die gewünschte Genauigkeit bei der Laserspektroskopie zu erreichen, muss ein effizienter und schneller Kühlprozess für die injizierten hochegeladenen Ionen realisiert werden. Dies kann mittels sympathetischer Kühlung in einer lasergekühlten Wolke leichter Ionen realisiert werden. Im Rahmen dieser Arbeit wurde ein Lasersystem und eine Ionenquelle für die Produktion einer solchen 24Mg+ Ionenwolke aufgebaut und erfolgreich an SPECTRAP in Betrieb genommen. Dazu wurde ein Festkörperlasersystem für die Erzeugung von Licht bei 279.6 nm entworfen und aufgebaut. Es besteht aus einem Faserlaser bei 1118 nm der in zwei aufeinanderfolgenden Frequenzverdopplungsstufen frequenzvervierfacht wird. Die Verdopplerstufen sind als aktiv stabilisierte Resonantoren mit nichtlinearen Kristallen ausgelegt. Das Lasersystem liefert unter optimalen Bedingeungen bis zu 15 mW bei der ultravioletten Wellenlänge und erwies sich während der Teststrahlzeiten an SPECTRAP als ausgesprochen zuverlässig. Desweiteren wurde eine Ionequelle für die gepulste Injektion von Mg+ Ionen in die SPECTRAP Falle entwickelt. Diese basiert auf der Elektronenstoßionisation eines thermischen Mg-Atomstrahls und liefert in der gepulsten Extraktion Ionenbündel mit einer kleinen Impuls- und Energieverteilung. Unter Nutzung des Lasersystems konnten damit an SPECTRAP erstmals Ionenwolken mit bis zu 2600 lasergekühlten Mg Ionen erzeugt werden. Der Nachweis erfolgte sowohl mittels Fluoreszenz als auch mit der FFT-ICR Technik. Aus der Analyse des Fluoreszenz-Linienprofils lässt sich sowohl die Sensitivität auf einzelne gespeicherte Ionen als auch eine erreichte Endtemperatur in der Größenordnung von ≈ 100 mK nach wenigen Sekunden Kühlzeit belegen.

The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.