We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
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.
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.
We study the stability of vortices in trapped single-component Bose–Einstein condensates within self-consistent mean-field theories; in particular, we consider the Hartree–Fock–Bogoliubov–Popov theory and its recently proposed gapless extensions. It is shown that for sufficiently repulsively interacting systems the anomalous negative-energy modes related to vortex instabilities are lifted to positive energies due to partial filling of the vortex core with noncondensed gas. Such behaviour implies that within these theories the vortex states are eventually stable against the transfer of condensate matter to the anomalous core modes. This self-stabilization of vortices, shown to occur under very general circumstances, is contrasted to the predictions of the non-self-consistent Bogoliubov approximation, which is known to exhibit anomalous modes for all vortex configurations and thus implying instability of these states. In addition, the shortcomings of these approximations in describing the properties of vortices are analysed, and the need for a self-consistent theory taking properly into account the coupled dynamics of the condensate and the noncondensate atoms is emphasized.
We compute structures of vortex configurations in a harmonically trapped Bose-Einstein condensed atom gas within three different gapless self-consistent mean-field theories. Outside the vortex core region, the density profiles for the condensate and the thermal gas derived from the Hartree-Fock-Bogoliubov-Popov theory are found to differ by only a few per cent from those derived from two of its recently proposed gapless extensions. In the core region, however, the differences between the density profiles are substantial. The structural differences are reflected in the energies of the quasiparticle states localized near the vortex core. In particular, the predictions for the energy of the lowest quasiparticle excitation derived from the theoretical models investigated differ considerably.
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.
We review the theory of vortices in trapped dilute Bose-Einstein condensates and compare theoretical predictions with existing experiments. Mean-field theory based on the time-dependent Gross-Pitaevskii equation describes the main features of the vortex states, and its predictions agree well with available experimental results. We discuss various properties of a single vortex, including its structure, energy, dynamics, normal modes, and stability, as well as vortex arrays. When the nonuniform condensate contains a vortex, the excitation spectrum includes unstable (`anomalous') mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex. We consider the effect of thermal quasiparticles on vortex normal modes as well as possible mechanisms for vortex dissipation. Vortex states in mixtures and spinor condensates are also discussed.