In this chapter a basic introduction to the theory of vortices in ultra-cold (superfluid) atomic gases is given. The main focus will be on bosonic atomic gases, since these contain the same basic physics, but with simpler formulas. Towards the end of the chapter, the difference between bosonic and fermionic atomic gases is discussed. This discussion will allow the reader to make the conceptual step from bosonic to fermionic gases, while pinpointing the main differences and difficulties when working with fermionic gases rather than bosonic gases. The goal of this chapter is to provide a good and general starting point for researchers, or other interested parties, who wish to start exploring the physics of ultra-cold gases.
Part of the book: Vortex Dynamics and Optical Vortices
In this chapter, we present the details of the derivation of an effective field theory (EFT) for a Fermi gas of neutral dilute atoms and apply it to study the structure of both vortices and solitons in superfluid Fermi gases throughout the BEC-BCS crossover. One of the merits of the effective field theory is that, for both applications, it can provide some form of analytical results. For one-dimensional solitons, the entire structure can be determined analytically, allowing for an easy analysis of soliton properties and dynamics across the BEC-BCS interaction domain. For vortices on the other hand, a variational model has to be proposed. The variational parameter can be determined analytically using the EFT, allowing to also study the vortex structure (variationally) throughout the BEC-BCS crossover.
Part of the book: Superfluids and Superconductors