## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Technology to be presented with due
permission for public examination and debate in Auditorium F1 at Helsinki
University of Technology (Espoo, Finland) on the
10^{th} of January, 2003, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-6066-2) [4708 KB]

Dissertation is also available in print (ISBN 951-22-6065-4)

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.

In 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.

This 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.

Singly 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.

This thesis consists of an overview and of the following 6 publications:

- S. M. M. Virtanen, T. P. Simula, and M. M. Salomaa, Structure and Stability of Vortices in Dilute Bose-Einstein Condensates, Physical Review Letters 86, 2704 (2001). © 2001 American Physical Society. By permission.
- S. M. M. Virtanen, T. P. Simula, and M. M. Salomaa, Comparison of mean-field theories for vortices in trapped Bose-Einstein condensates, Journal of Physics A: Condensed Matter 12, L819 (2001). © 2001 IOP Publishing Ltd. By permission.
- S. M. M. Virtanen, T. P. Simula, and M. M. Salomaa, Adiabaticity Criterion for Moving Vortices in Dilute Bose-Einstein Condensates, Physical Review Letters 87, 230403 (2001). © 2001 American Physical Society. By permission.
- T. P. Simula, S. M. M. Virtanen, and M. M. Salomaa, Stability of multiquantum vortices in dilute Bose-Einstein condensates, Physical Review A 65, 033614 (2002). © 2002 American Physical Society. By permission.
- T. P. Simula, S. M. M. Virtanen, and M. M. Salomaa, Surface modes and vortex formation in dilute Bose-Einstein condensates at finite temperatures, Physical Review A, 66, 035601 (2002). © 2002 American Physical Society. By permission.
- T. P. Simula, S. M. M. Virtanen, and M. M. Salomaa, Quantized Circulation in Dilute Bose-Einstein Condensates, Computer Physics Communications 142, 396 (2001). © 2001 Elsevier Science. By permission.

Errata of publications 1 and 4

**Keywords:**
Bose-Einstein condensate, vortex, superfluidity, mean-field theory,
quasiparticle

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© 2002 Helsinki University of Technology

Last update 2011-05-26