During the last decade the physics of ultracold quantum gases has matured into a highly active and versatile field of research. Experiments dedicated to the physics of Bose-Einstein condensates have been performed and diverse phenomena, which are distinguished by fundamentally different regimes of interaction, can be investigated. Particularly solitons, characterized as non-spreading wavepackets, are stabilized against dispersion by a suitable non-linear interaction and can propagate in a condensate[1,2]. In the present work the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics for the first time. We have been able to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency of ω/√2 has been obtained [1]. Moreover the results of detailed studies of the collision of two dark solitons distinguished by different depths are presented. This particular feature enables the identification of the individual solitons beyond the actual collision process and as a central result we show shown that these peculiar entities interpenetrate without significantly influencing each other [3]. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial “dark-bright” solitons and their dynamical properties complement the investigations on dark solitons.
During the last decade the physics of ultracold quantum gases has matured into a highly active and versatile field of research. Experiments dedicated to the physics of Bose-Einstein condensates have been performed and diverse phenomena, which are distinguished by fundamentally different regimes of interaction, can be investigated. Particularly solitons, characterized as non-spreading wavepackets, are stabilized against dispersion by a suitable non-linear interaction and can propagate in a condensate[1,2]. In the present work the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics for the first time. We have been able to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency of ω/√2 has been obtained [1]. Moreover the results of detailed studies of the collision of two dark solitons distinguished by different depths are presented. This particular feature enables the identification of the individual solitons beyond the actual collision process and as a central result we show shown that these peculiar entities interpenetrate without significantly influencing each other [3]. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial “dark-bright” solitons and their dynamical properties complement the investigations on dark solitons.
During the last decade the physics of ultracold quantum gases has matured into a highly active and versatile field of research. Within the framework of this thesis experiments dedicated to the physics of Bose-Einstein condensates have been performed and diverse phenomena, which are distinguished by fundamentally different regimes of interaction, could be investigated. For the first time the dynamical evolution of long-lived dark solitons has been studied as a paradigm of non-linear physics. Solitons, characterized as non-spreading wave packets, are stabilized against dispersion by a suitable non-linear interaction. It has been possible to observe oscillations of dark solitons in elongated Bose-Einstein condensates and good agreement with the theoretically predicted oscillation frequency has been obtained. Moreover experiments have been conducted which address the collision of two dark solitons distinguished by different depths. This particular feature enabled the identification of the individual solitons beyond the actual collision process and as a central result it could be shown, that these peculiar entities interpenetrate without significantly influencing each other. The theoretical description of solitons as weakly interacting quasi particles is in good agreement with these findings. Continuative studies on vectorial dark-bright solitons and their dynamical properties complement the investigations on dark solitons. A central goal of this dissertation has been the design and implementation of an optical lattice with an underlying triangular symmetry in order to investigate strongly correlated ultracold atoms in a novel experimental geometry. Exhibiting an explicit polarization dependence the optical lattice realized here should allow for the creation and analysis of thus far unexplored magnetic phases. Experiments attending to the quantum phase transition from a superfluid to a Mott-insulating state in a three- as well as in a two-dimensional system with triangular symmetry have been performed. Similarities as well as differences to the findings obtained in cubic lattices have been worked out and could be attributed to the inherent differences in the crucial lattice parameters such as tunneling energy J and onsite interaction U. Devoted to the dynamics of spinor condensates, a third part of this thesis concerns the physics of multi component quantum gases. Employing suitable spin-independent trapping potentials the physics of Bose-Einstein condensates may be extended to the investigation of the static and dynamical properties of internal degrees of freedom, in this case the spin of the atoms. The measurements presented here concentrate on the coherent dynamical evolution of the vectorial order parameter of a spinor condensate. Rb condensates with F=1 and F=2 have been studied and the existence of a spin dynamics resonance, caused by the competition between spin-dependent non-linear interaction and quadratic Zeeman effect was demonstrated for the first time.
Die Physik ultrakalter Quantengase stellt sich heutzutage als ein hochaktives und vielseitiges Forschungsfeld dar. Im Rahmen dieser Dissertation konnten fundamentale Erkenntnisse zu unterschiedlichen Phanomenen in Bose-Einstein Kondensaten gewonnen werden, welche vollig verschiedenen Wechselwirkungsbereichen zuzuordnen sind. Erstmals wurden Experimente durchgefuhrt, die als eines der Paradigmen nichtlinearer Physik die Dynamik extrem langlebiger dunkler Solitonen zeigen. Solitonen, die sich als formstabile Wellenpakete auszeichnen, resultieren aus einer Kompensation der Dispersion durch eine entgegengerichtet wirkende nichtlineare Wechselwirkung. Oszillationen von dunklen Solitonen in elongierten Bose-Einstein Kondensaten wurden beobachtet und eine sehr gute ubereinstimmung mit der theoretisch erwarteten Oszillationsfrequenz wurde gefunden. Desweiteren konnten im Verlauf dieser Arbeit Experimente durchgefuhrt werden, bei denen die Kollisionen unterschiedlich tiefer dunkler Solitonen untersucht wurden. Es war dadurch moglich die Solitonen uber den Kollisionszeitpunkt hinaus zu verfolgen. Als ein zentrales Ergebnis wurde gezeigt, dass Solitonen sich im Verlauf der Kollision durchdringen ohne einen nennenswerten Einfluss aufeinander auszuuben, was in ubereinstimmung mit der theoretischen Beschreibung von Solitonen als schwach wechselwirkende Quasiteilchen steht. Daruber hinaus konnten diese Studien durch Untersuchungen an 'gefullten' Solitonen abgerundet werden. Als ein wesentliches Forschungsziel wurde im Verlauf dieser Dissertation ein optisches Gitter mit einer Dreieckssymmetrie aufgebaut, um die experimnetelle Grundlage fur die Untersuchung stark korrelierter ultrakalter Atome in einer neuartigen Geometrie zu schaffen. Es konnte eine Polarisationsabhangigkeit des periodischen Potentials herausgestellt werden, welche die Untersuchung neuartiger magnetischer Phasen ermoglichen sollte. Experimente zum Quantenphasenubergang zwischen Superfluid und Mott-Isolator in drei- als auch zweidimensionalen Systemen mit Dreieckssymmetrie wurden durchgefuhrt und analysiert. Unterschiede als auch Gemeinsamkeiten zu fruheren Ergebnissen, die in kubischen Gittern gewonnen wurden, konnten nachgewiesen und auf Unterschiede der entscheidenden Gitterparameter, wie etwa Tunnelenergie und Wechselwirkung, zuruckgefuhrt werden. Ein weiterer Teil der vorliegenden Arbeit widmet sich Untersuchungen zur Dynamik von mehrkomponentigen Spinor Bose-Einstein Kondensaten. In entsptrechend spinunabhangigen Fallenpotentialen, wie sie durch optische Dipolfallen realisiert werden konnen, lasst sich die Physik Bose-kondensierter Materie auf eine zusatzliche Dynamik der inneren Freiheitsgrade, in diesem Fall des Spins, erweitern. Die im Rahmen dieser Dissertation durchgefuhrten Experimente zur Physik mehrkomponentiger Quantengase konzentrieren sich auf die koharente zeitliche Entwicklung des vektoriellen Ordnungsparameters eines Spinor Kondensates, gemeinhin als Spindynamik bezeichnet. Rb Kondensate mit Spin-1 als auch Spin-2 wurden untersucht und als ein zentrales Ergebnis konnte erstmals eine Spindynamikresonanz vermessen werden, welche aus der Konkurrenz zwischen spinabhangiger Wechselwirkung and quadratischem Zeemaneffekt heraus entsteht.
We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.
Abstract: In this thesis we experimentally observe the dynamics of dark solitons in elongated Bose-Einstein condensates (BEC) in the crossover regime between 1D and 3D. Dark solitons are dynamically stable in this regime. This allows the observation of the collisional and oscillational dynamics of two dark solitons in a harmonically confined BEC over several oscillation periods. We can detect the repulsive intersolitonic interaction as an increase of the oscillation frequency of the two solitons strongly depending on their mean distance. Thereby we give the first experimental evidence of the theoretically predicted repulsive interaction between the solitons. We compare our experimental findings to numerical simulations of the Gross-Pitaevskii equation and effective 1D equations. Additionally we develop a model in which the solitons are approximated by repulsively interacting classical particles. This model is based on a soliton interaction potential suggested by [Kiv1995] and can describe the essentials of the soliton dynamics. We observe well agreement between the soliton oscillation frequencies measured in the experiment, the numerical simulations and the results of the particle model. Besides we verify the theoretical prediction that the oscillation frequency of dark solitons in a harmonically confined BEC should be slower than the trap frequency.
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrodinger equation, the so-called Gross-Pitaevskii (GP) equation, which is a mean-field description of BECs. The systematic analysis begins by considering the dark-bright (DB)-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component BECs. The interaction between two DB solitons in a homogeneous condensate and at the presence of the trap are both considered. Our analytical approximation relies in a Hamiltonian perturbation theory, which leads to an equation of motion of the centers of DB-soliton interacting pairs. Employing this equation, we demonstrate the existence of robust DB-soliton molecules, in the form of stationary two- and three-DB-soliton states. Also the equilibrium distance of the constituent solitons and the corresponding oscillation frequencies are found semianalytically, where the latter corresponds to the characteristic anomalous modes' eigenfrequencies that we numerically computed via a so called Bogoliubov-de Gennes (BdG) linearization analysis. Those studies are discussed in Chapter 2. Then, we extend our studies to the dynamics of dark-bright (DB) solitons in binary BECs at finite temperature using a system of two-coupled dissipative GPs. We show that the effect of the bright soliton is to partially stabilize dark solitons against temperature-induced dissipation, thus providing longer lifetimes in Chapter 3. Furthermore, the dark-dark (DD) solitons as a prototypical coherent structure that emerges in two-component BECs are studied and are connected to dark-bright (DB) solitons via SO(2) rotation. We obtained their beating frequency and their frequency of oscillation inside a parabolic trap. They are identified as exact periodic orbits in the Manakov limit of equal inter- and intra- species nonlinearity strengths with and without the trap and we showcase the persistence of such states upon weak deviations from this limit. Also we investigated in detail the effect of the deviation from the Manakov case by considering different from unity scattering length ratios in Chapter 4. Next, we revisited Hamiltonian eigenvalue problems that typically arise in the linearization around a stationary state of a Hamiltonian nonlinear PDE. Also we presented a overview of the known facts for the eigenvalue counts of the corresponding unstable spectra. In particular, we focused on a straightforward plan to implement finite-dimensional techniques for locating this spectrum via the singular points of the meromorphic Krein Matrix and illustrated the value of the approach by considering realistic problems for recently observed experimentally multivortex and multisoliton solutions in atomic Bose-Einstein condensates in Chapter 5. In the two dimensional scenario, we also examine the stability and dynamics of vortices under the effect of dissipation used as a simplified model for the inclusion of the effect of finite temperatures in atomic BECs, which enables an analytical prediction that can be compared directly to numerical results in Chapter 6. In all the above studies, our analytical prediction from the equation of motion are in good agreement with the numerical results from the BdG analysis.