Bose-Einstein condensation, first predicted by Bose and Einstein in 1924, was finally realized in dilute, weakly interacting gases of alkali atoms in 1995. A few years later, quantized vortices - intimately related to the phenomenon of superfluidity - were created and observed in these novel quantum many-body systems.\n\nIn this Thesis, vortices in dilute atomic Bose-Einstein condensates are studied theoretically and computationally using microscopic mean-field theory formalisms. Special emphasis is on the structure and the stability of vortices at finite temperatures. The formation of quantized circulation in Bose-Einstein condensates is investigated, as well as multiply quantized vorticity and the adiabaticity of the precessing motion of a vortex.\n\nThis research strongly relies on numerically solving the Gross-Pitaevskii equation for the macroscopic condensate wavefunction and the coupled Bogoliubov equations and their variants for the collective quasiparticle excitation eigenmodes. The computed elementary excitation spectra are used, for instance, in determining the local stability of various condensate states. The vortex formation process is studied at finite temperatures in terms of the surface modes of the condensate providing the Landau critical velocities for the breakdown of superfluidity. Free energy calculations are used for determining the thermodynamic equilibrium states.\n\nSingly quantized, axisymmetric vortex states are found to be locally energetically stable even in the zero-temperature limit within the self-consistent finite-temperature approximations. This would imply for the vortex a precession direction opposite to that observed in the experiment. Adiabatic approximation of quantum mechanics is formulated for Bose-Einstein condensed systems and is applied to a case of a moving vortex line. The experimentally observed precessing motion of the vortex is found to be nonadiabatic. A method to create stable multiply quantized vortices using an additional pinning potential is presented. The computed critical trap rotation frequencies for vortex nucleation at finite temperatures are in agreement with experiments and the predictions of zero-temperature field theories.
Bose-Einstein condensation, first predicted by Bose and Einstein in 1924, was finally realized in dilute, weakly interacting gases of alkali atoms in 1995. A few years later, quantized vortices - intimately related to the phenomenon of superfluidity - were created and observed in these novel quantum many-body systems.\n\nIn this Thesis, vortices in dilute atomic Bose-Einstein condensates are studied theoretically and computationally using microscopic mean-field theory formalisms. Special emphasis is on the structure and the stability of vortices at finite temperatures. The formation of quantized circulation in Bose-Einstein condensates is investigated, as well as multiply quantized vorticity and the adiabaticity of the precessing motion of a vortex.\n\nThis research strongly relies on numerically solving the Gross-Pitaevskii equation for the macroscopic condensate wavefunction and the coupled Bogoliubov equations and their variants for the collective quasiparticle excitation eigenmodes. The computed elementary excitation spectra are used, for instance, in determining the local stability of various condensate states. The vortex formation process is studied at finite temperatures in terms of the surface modes of the condensate providing the Landau critical velocities for the breakdown of superfluidity. Free energy calculations are used for determining the thermodynamic equilibrium states.\n\nSingly quantized, axisymmetric vortex states are found to be locally energetically stable even in the zero-temperature limit within the self-consistent finite-temperature approximations. This would imply for the vortex a precession direction opposite to that observed in the experiment. Adiabatic approximation of quantum mechanics is formulated for Bose-Einstein condensed systems and is applied to a case of a moving vortex line. The experimentally observed precessing motion of the vortex is found to be nonadiabatic. A method to create stable multiply quantized vortices using an additional pinning potential is presented. The computed critical trap rotation frequencies for vortex nucleation at finite temperatures are in agreement with experiments and the predictions of zero-temperature field theories.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
Since the first realizations of Bose-Einstein condensation in dilute alkali-atom vapours in 1995, these novel quantum gases have attracted wide interest. The main focus of the research has been on finding out the coherence and superfluidity properties of the condensates. From the theoretical point of view, these systems provide a rare possibility to model an interacting many-particle system exhaustively and quantitatively accurately from first-principles quantum field theories. However, the challenge of developing a correct and computationally feasible finite-temperature formalism still remains.\n\nThe coherence and superfluidity properties are intimately related to the existence and stability of quantized vortices. In this thesis, the structure and stability of vortex states in weakly interacting Bose-Einstein condensates is investigated within microscopic finite-temperature mean-field theories. An effective scheme for computationally solving the Bogoliubov-de Gennes quasiparticle eigenequations is developed, and applied to study the microscopic structure of vortex states in partially condensed vapours. In contrast to experimental observations and the predictions of the zero-temperature Bogoliubov approximation, stationary vortex states are found to be metastable within the self-consistent Popov approximation and its extensions even in the zero-temperature limit.\n\nThe reasons underlying this discrepancy are analysed in detail. A criterion for the validity of stationary mean-field approximations in modelling slowly time-dependent systems is derived, and applied to precessing off-axis vortex states. Under typical experimental conditions moving vortices are shown to be deformed due to the inability of the thermal cloud to follow the vortex core rigidly. Consequently, the validity of the commonly used stationary mean-field theories in describing such states is shown to be questionable. Finally, an analysis of uniformly precessing off-axis vortex states within a fully time-dependent Popov approximation is presented. Even dynamically deformed vortices are shown to become energetically metastable as the vortex core is partially filled with noncondensed gas in the course of thermalization. This self-stabilization mechanism of vortex states, shown to occur under very general circumstances, is an inherent property of all self-consistent formalisms having a structure similar to the Popov approximation. However, it is argued to be affected by the improper treatment of the noncondensate dynamics within these formalisms, and the need for a theory taking properly into account the coupled dynamics of the condensate and the noncondensate in modelling vortex states is emphasized. The computational scheme developed is also applied to investigate possibilities to energetically stabilize multiply quantized vortex states by piercing an externally rotated condensate with a blue-detuned laser beam.
The condensation of weakly interacting alkali atom gases observed in 1995 is a manifestation of the macroscopic quantum phenomenon called Bose-Einstein condensation. In contrast to superconductivity and Helium superfluids, the dilute alkali atom condensates are directly observable using optical imaging techniques and they constitute highly controllable quantum systems. Hence, they offer an ideal test bench to investigate the applicability of quantum field theories and to predict the properties of the condensates starting from the first principles.\n\nSince the first experimental realizations of dilute Bose-Einstein condensates, a great interest has been focused on this field, resulting in numerous experimental studies concerning, for example, nonlinear dynamics and the elementary excitations of these many-particle quantum systems. The existence of topological phase singularities, quantized vortices, first predicted theoretically and finally observed experimentally in 1999, led to another series of pioneering theoretical and experimental studies.\n\nSeveral methods to create single-quantum vortices were realized already in 2001 but, however, the puzzle of creating multiply quantized vortices still remained. In this thesis, the so-called topological method to create two and four times quantized vortices is studied in detail. Since the instrumentation required for the experimental realization of the topological method had already been installed in many laboratories, the theoretical predictions of this thesis were experimentally verified shortly after their publication. Multiply quantized vortices are energetically unstable and tend to split into singly quantized vortices. However, the dissipation of energy in the condensates is minimal at low temperatures and, consequently, can lead to long lifetimes for the multiquantum vortices. Nevertheless, one prediction of this thesis is that the lifetimes of doubly quantized vortices are relatively short, owing to the known dynamical instability of the state. The splitting of the doubly quantized vortex has recently been observed experimentally.\n\nThe stability of vortices in dilute Bose-Einstein condensates is intimately related to the excitation spectrum of the stationary vortex state. However, developing an accurate, computationally feasible finite-temperature quantum field theory remains an open problem. In this thesis, we study the elementary excitations of an irrotational condensate within a recently developed systematic second order perturbation theory. The collapse and revival of certain elementary excitations is discovered.\n\nThe most recent studies of this thesis are devoted to stationary, but rotationally asymmetric vortex states. In weakly interacting condensates, a novel stationary state, a vortex tripole holding finite angular momentum is presented. Also the lowest elementary excitations of the so-called vortex dipole, tripole, and quadrupole states are studied.
In 1995, atomic physics took a quantum leap with the experimental discovery of almost ideal Bose-Einstein condensation in dilute gases of alkali atoms. The gaseous condensates offer a rare chance to study an interacting many-particle system accurately from first-principles theories, and they can be used to simulate many seminal models that have proven elusive in their original context of, e.g., solid-state or high-energy physics. An important topic in the research has been the quantized vortex, which was experimentally realized in 1999 and whose existence is intimately related to the concepts of quantum phase coherence and superfluidity.\nIn this dissertation, unconventional vortex structures are investigated in the dilute condensates at ultralow temperatures. A combination of analytical and numerical methods is used to examine the structure, stability, and dynamical behavior of multiquantum vortices and vortex-antivortex pairs in spin-polarized condensates, unusual vortex lattices in two-species condensates, and spin textures in condensates with dipolar interactions. In studying the properties of the multiquantum vortices, particular emphasis is placed on exploring the practical limits of producing them through adiabatic pumping of vorticity. The majority of the research is conducted by solving the mean-field Gross-Pitaevskii and Bogoliubov equations.\nVarious original, experimentally verifiable results concerning the exotic vortex structures are presented. Novel splitting patterns of vortices with large quantum numbers are introduced, and it is shown that such vortices can be feasibly stabilized by piercing them with a focused laser beam. A recent experiment on vortex-antivortex pairs is simulated, and an excellent quantitative agreement with the experimental data is obtained. Unconventional ground-state vortex lattices, such as ones having a square geometry or consisting of two-quantum vortices, are shown to exist in rotating two-species condensates. Dipolar interactions are found to support helical spin-vortex states, and the energies of spin-wave excitations are observed to increase rapidly with the dipolar coupling strength.\nThis dissertation contributes to the understanding of superfluid phenomena in Bose-Einstein condensates and has significant implications for the prospects of detecting novel vortex structures in current experiments.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.
In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)