Topological deflects and phase transitions in dilute Bose gases

Since the discovery of Bose-Einstein condensation in dilute atomic vapours in 1995, there has been a monumental increase in the research effort in the field of atomic physics due to the unforeseen opportunities and challenges that the degenerate quantum gases present. In particular, quantum gases can emulate complicated models that arise in solid state and high energy physics, allowing realisations of exotic phenomena that have proven to be elusive in their original context. An outstanding example is the existence of various topological defects in degenerate quantum gases with internal degrees of freedom. Topological excitations such as skyrmions and several types of monopoles can be shown to take place in Bose gases with a hyperfine spin degree of freedom as a result of a coupling to an external field or due to thermal fluctuations. A central question in the context of dilute Bose gases is the relation between superfluidity and Bose-Einstein condensation. The dimensionality of the underlying space as well as the internal degrees of freedom have a direct impact on the existence and the nature of the Bose-Einstein condensate. For example, any uniform Bose gas in two spatial dimensions or an antiferromagnetic spinor Bose gas can give rise to a superfluid state which does not involve a conventional Bose-Einstein condensate corresponding to a single macroscopically occupied quantum state. In this Thesis, properties of different topological defects and their relation to superfluidity in dilute Bose gases are investigated. Stability and creation of coreless vortices are first studied and a method to cyclically increase the angular momentum of the condensate is introduced. Subsequently, the properties and creation of different types of monopoles are investigated and an experimentally feasible method to create a Dirac monopole is presented. Finally, finite temperature phase transitions in quasi-two-dimensional Bose gases with a spin degree of freedom are analysed and, as a related subject, the stability of vortex clusters formed by vortices and antivortices is studied.