In this thesis, we study the dynamics of ultracold quantum gases with respect to micro-gravity experiments, discuss interferometric applications and aspects on collective scattering. We describe the dynamics of an ultracold quantum gas in a long-distance free-fall experiment, which is of relevance for the present QUANTUS experiment. We develop the quantum field theoretical description of a trapped, interacting degenerate quantum gas in a drop experiment in an inertial frame, the corotating frame of the Earth and the comoving frame of the drop capsule. This formalism provides us with an efficient description of the experiment, especially for numerical studies. Moreover, we review the ideas of gravitational sensing with the help of an interferometric setup. We show that in case of a spatially quasi-homogeneous condensate the same results as in single-atom interferometry can be obtained even in the presence of a nonlinear time evolution. A decline of the contrast in an interferogram is found, though. In addition, we propose a rotational sensor based on a superposition of a non-rotating state and a quantized vortex in a Bose-Einstein condensate. As an application for an interferometric experiment in a micro-gravity environment, we establish a number filter for matter waves. Our number filter allows for a number stabilization, i.e. after passing the filter, the number uncertainty is less than before. This can be achieved by using a nonlinear matter wave interferometer for a two-component BEC. An asymmetric splitting is required in order to observe the effect. Finally, we examine the collective scattering of a superfluid droplet impinging on a two-component Bose-Einstein condensate. We demonstrate that this mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles. We obtain resonant scattering phase shifts from a linear response theory. We find an energy-dependent transmission coefficient that is controllable between 0 and 100%.
In this thesis, we study the dynamics of ultracold quantum gases with respect to micro-gravity experiments, discuss interferometric applications and aspects on collective scattering. We describe the dynamics of an ultracold quantum gas in a long-distance free-fall experiment, which is of relevance for the present QUANTUS experiment. We develop the quantum field theoretical description of a trapped, interacting degenerate quantum gas in a drop experiment in an inertial frame, the corotating frame of the Earth and the comoving frame of the drop capsule. This formalism provides us with an efficient description of the experiment, especially for numerical studies. Moreover, we review the ideas of gravitational sensing with the help of an interferometric setup. We show that in case of a spatially quasi-homogeneous condensate the same results as in single-atom interferometry can be obtained even in the presence of a nonlinear time evolution. A decline of the contrast in an interferogram is found, though. In addition, we propose a rotational sensor based on a superposition of a non-rotating state and a quantized vortex in a Bose-Einstein condensate. As an application for an interferometric experiment in a micro-gravity environment, we establish a number filter for matter waves. Our number filter allows for a number stabilization, i.e. after passing the filter, the number uncertainty is less than before. This can be achieved by using a nonlinear matter wave interferometer for a two-component BEC. An asymmetric splitting is required in order to observe the effect. Finally, we examine the collective scattering of a superfluid droplet impinging on a two-component Bose-Einstein condensate. We demonstrate that this mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles. We obtain resonant scattering phase shifts from a linear response theory. We find an energy-dependent transmission coefficient that is controllable between 0 and 100%.
We analyze the evolution of a degenerate quantum gas (bosons and fermions) falling in Earth's gravity during long times (10s) and over large distances (100m). This models an experiment that is currently performed by the QUANTUS Collaboration at ZARM drop tower in Bremen, Germany. Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop a quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate noninertial forces, provided all external potentials (trap, gravity) can be approximated with a second-order Taylor expansion around the instantaneous trap center. This is an excellent assumption, and the harmonic potential theorem applies. As a first application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest frame of the superfluid wave packet, the long-distance drop can be studied easily on a numerical grid.
Inertial sensors based on matter-wave interferometry are currently approaching the precision and accuracy of state-of-the-art classical sensors. While these devices are often realised with ultracold but not Bose-condensed atoms as matter waves, employing Bose-Einstein Condensates (BEC) promises to overcome certain limitations, especially those related to the ensemble's expansion. The point-source like character of BECs also enables utilising spatial interference patterns to measure e.g. rotation rates in single-shot experiments. Matter wave-based inertial sensors are considered for experiments ranging from Gravitational Wave detection to tests of the Universality of Free Fall (UFF) to gain insight into the joint between Quantum Mechanics and General Relativity. In the scope of this thesis, matter-wave interferometry with BECs was demonstrated for the first time in a microgravity environment with the QUANTUS-1 apparatus. The same instrument was then employed as a quantum tiltmeter utilising a novel beam-splitting mechanism known as Bragg Double Diffraction. To this end, the QUANTUS-1 apparatus designed as a BEC instrument to be operated in the drop tower at ZARM at University of Bremen was equipped with optics and laser systems required for performing matter-wave interferometry based on Bragg Diffraction. The apparatus employs an atom chip to create BECs of around 10000 Rubidium 87 atoms within 15 s. With a Mach-Zehnder like interferometer scheme, spatial interference fringes were observed after a free evolution time in the interferometer of up to 677 ms. To achieve these long time scales, a method known as Delta-Kick Collimation (DKC) was adapted to slow the expansion of the BEC to a kinetic energy equivalent below 1 nK, and the atoms were transferred to a non-magnetic Zeeman state via an adiabatic rapid passage (ARP). A similar interferometer scheme with a newly developed beam-splitter mechanism known as Bragg Double Diffraction was used to measure the tilt of the instrument on ground with a precision of up to 4.4 AA rad. This thesis presents an overview of the apparatus including ground-based characterisations of all required experimental steps. Results from over 400 free fall experiments are evaluated for expansion studies of the BEC and matter-wave interferometry in microgravity. The time-evolution of first and second order Bragg Double Diffraction beam splitters is studied, and an interferometer sensitive to the tilt of the instrument is implemented. Based on this work, a gravimeter with a new launch mechanism comprising Bragg beam splitters and Bloch oscillations to enable atomic fountains in atom-chip based devices was developed. The microgravity experiments were adapted for the MAIUS-1 sounding-rocket instrument to create the first man-made BEC in outer space and study the feasibility of operating matter-wave interferometers on space-borne platforms. The results of this thesis lay the groundwork for future space-borne missions using matter-wave interferometry for precision measurements of inertial forces.
Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
In the years following the first Bose-Einstein condensation of dilute atomic gases in 1995, several experiments demonstrated many fundamental properties of two-component BEC. Subsequent to these pioneering experiments, almost a decade passed with little experimental activity, relative to investigations of single-component condensates. In somewhat of a renaissance, the initial observations of two-component BEC have been revisited in recent years, consolidating and clarifying results of the early works, and illuminating new and surprising behaviour of these rich quantum fluids. This thesis presents new experimental results on the relative phase evolution of two-component Bose-Einstein condensates (BECs). We approach our study of this system from the dual perspective of binary superfluidity and trapped atom interferometry. We observe nonequilibrium dynamics of the condensate that are deeply connected to the physics of interpenetrating superfluids. These dynamics have consequences for interferometers whose two paths are different internal spin states of the condensate atoms. Using trapped condensates for precision measurement draws upon the benefits of confined atom interferometry - long interrogation times, precise position control to measure near-field potentials - in addition to the unique coherence properties of BECs. Precision measurementwith trapped particles, however, is obstructed by the inherent inhomogeneities associated with the confinement itself. Spatial variation of the external potentials and atomic density can give rise to dephasing during the free evolution and imperfect splitting and recombination of the interferometric paths. In this thesis, we consider the dephasing of the two-componentmean field order parameter, which tends to diminish the interference signal attained with the condensate. The promise of fuhs for atom interferometry lies within using nonclassical many body states to reduce the fundamental noise limit imposed upon measuring the projection of atomic pseudospin. Before the many body quantum properties of two-component condensates can be used to their full potential, the ideal classical limit must be achieved and investigated. As in optical interferometry, the classical ideality of an interference measurement is contingent upon control of the spatialmodes - thematter wave fields, or single particle wave functions. Whilst much attention is currently focused on preparing nonclassical many body states for entanglement and squeezing of the condensate pseudospin, this thesis focuses on the ancillary yet important issue of spatial inhomogeneity of the condensate mean field. Reversal of the spatially inhomogeneous mean field evolution is demonstrated, employing the techniques of nuclear magnetic resonance. A new method is demonstrated to probe pseudospin -1/2 condensates involving microwave adiabatic passage. The technique permits simultaneous, spatially resolved absorption imaging of the spatial mode of each component. Controlled manipulation of the components into Zeeman states with different magnetic moments allows spatial separation using a Stern-Gerlach separation technique, providing a spatially resolved projection of the local condensate pseudospin from a single absorption image. We propose an interferometric technique which employs this imaging method to directly image the relative phase. The miscibility of the two components depends on the relative magnitude of the interactions between various collision partners. The boundary of this miscibility is found to be less pronounced than expected from the commonly applied results of homogeneous super-fluids.The effects of kinetic energy are shown to be significant at the threshold of miscibility, leading to a breakdown in the Thomas-Fermi approximation. Magnetic dipole transitions amongst alkali ground states are often used to prepare, manipulate, and interrogate pseudospin -1/2 condensates. We present a thorough investigation of the two-photonmagnetic dipole transitions between the |F = 1,mF = -1〉 and |F = 2,mF = +1〉 states, and the |F = 1,mF = +1〉 and |F = 2,mF = -1〉 states of 87Rb. Taking into account all 8 Zeeman levels of the electronic ground state reveals markedly different radiative shifts and effects beyond the rotating wave approximation, compared to the three-level formalism commonly used for these transitions.This has implications for Ramsey interferometry using the two-photon magnetic dipole transitions. The unchartered experimental territory offered by two-component condensates is vast, and future directions, supplementary to the work in this thesis, are elucidated.
Microgravity is expected to be a decisive ingredient for the next leap for experiments testing the fundamental physics of gravity, relativity and theories beyond the standard model. A promising technique for such tests in the quantum domain are matter-wave sensors based on cold atoms or atom lasers, which use atoms as unperturbed microscopic test bodies for measuring inertial forces or as frequency references. For matter-wave interferometers and experiments with quantum matter (Bose-Einstein Condensates or degenerate Fermi gases) microgravity allows the extension of the unperturbed free fall of these test particles in a low-noise environment.
In this habilitation-thesis a collection of 14 experiments is presented. In these experiments we have developed and used novel techniques to control ultracold gases on the quantum level. In brief, Bose-Einstein condensates (BEC) and degenerate Fermi gases of laser-cooled alkali atoms are subjected to specially designed optical and magnetic fields. The fields influence in a coherent way the behavior, properties and dynamics of the gases. On this basis we developed tools to prepare, coherently manipulate, and analyze pre-defined quantum states. With this high level of control, it was possible to investigate interesting physics phenomena, and we were able to achieve several breakthroughs in the field of ultracold atoms. Highlights of our experimental results include the demonstration of phase engineering of a BEC wavefunction where we created solitons in a BEC and studied their propagation. In another experiment we constructed a spatially resolved matter wave interferometer with which we mapped out the phase distribution on a condensate. Illuminating the BEC with a periodic pattern, i.e. an optical lattice, allowed us to study solid states physics phenomena. In a second set of experiments we demonstrated optically tuning of the interaction between atoms with optical Feshbach resonances. Employing either magnetically tunable Feshbach resonances or laser radiation, we were able to produce ground state molecules in well defined quantum states. This led to the production of the first molecular BEC. By tuning the coupling of atom pairs in a Fermi gas of atoms, we could for the first time investigate the so-called BEC-BCS crossover which describes the continuous change from a BEC superfluid to a Bardeen-Cooper Schrieffer (BCS) superfluid. Due to the excellent control on the quantum level, the developed cold atom techniques open up intriguing prospects for future applications and experiments. They represent a general tool box to investigate fundamental physical phenomena in a pure and undisturbed environment. In the future, cold atoms might serve as a testing ground for fundamental theories or as quantum simulators for complex systems.