## 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 Science in Technology to be presented with due permission of the
Department of Engineering Physics and Mathematics for public examination and debate in Auditorium
F1 at Helsinki University of Technology (Espoo, Finland) on the 27^{th} of December, 2004, at 14 o'clock.

Overview in PDF format (ISBN 951-22-7440-X) [2295 KB]

Dissertation is also available in print (ISBN 951-22-7439-6)

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.

Since 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.

Several 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.

The 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.

The 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.

This thesis consists of an overview and of the following 5 publications:

- Ogawa S.-I., Möttönen M., Nakahara M., Ohmi T., and Shimada H., 2002. Method to create a vortex in a Bose-Einstein condensate. Physical Review A 66, 013617. © 2002 American Physical Society. By permission.
- Möttönen M., Matsumoto N., Nakahara M., and Ohmi T., 2002. Continuous
creation of a vortex in a Bose-Einstein condensate with hyperfine spin
*F*= 2. Journal of Physics: Condensed Matter 14, number 49, pages 13481-13491. © 2002 Institute of Physics Publishing Ltd. By permission. - Möttönen M., Mizushima T., Isoshima T., Salomaa M. M., and Machida K., 2003. Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates. Physical Review A 68, 023611. © 2003 American Physical Society. By permission.
- Möttönen M., Virtanen S. M. M., Isoshima T., and Salomaa M. M., Stationary vortex clusters in nonrotating Bose-Einstein condensates. Physical Review A, submitted for publication. © 2004 by authors and © 2004 American Physical Society. By permission.
- Möttönen M., Virtanen S. M. M., and Salomaa M. M., Collapse and revival of excitations in Bose-Einstein condensates. Physical Review A, accepted for publication. © 2004 by authors and © 2004 American Physical Society. By permission.

**Keywords:**
Bose-Einstein condensation, vortex, non-linear phenomena

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© 2004 Helsinki University of Technology

Last update 2011-05-26