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.
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.
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.
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.
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.
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.
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.