The goal of creating and observing quantized vortices in trapped Bose gases arose almost immediately following the first achievements of Bose–Einstein condensation. The motivation for doing so was the obvious analogy with vortices in liquid helium and in type-II superconductors, and the fact that the quantization of circulation is directly associated with superfluid flow. It was recognized that the observation of quantized vortices could be taken as indisputable evidence for the existence of superfluidity in these systems.

The review by Fetter and Svidzinsky (2001) contains a summary of the early experiments and the theoretical background for understanding the vortex state in a weakly interacting Bose gas based on the GP equation. This material will not be repeated here apart from those aspects that have a direct bearing on the focus of the present chapter, namely the properties of vortices at finite temperature. Although there have been some theoretical contributions to this subject, much remains to be done. The discussion in this chapter provides a framework for addressing the finite-temperature properties of vortex formation and vortex lattices in the context of the ZNG theory. The results in this chapter have not been published before, apart from those in subsection 9.8.1, which are based on Williams et al. (2002).

There are several issues that relate to finite temperatures. First, there is the nucleation and formation of vortices from an initial highly nonequilibrium state. Second, there is the interaction of vortices with thermal excitations, which is responsible for the dissipative dynamics of a nonequilibrium vortex state. Third, there is the question of the final equilibrium state, with respect to the condensate and noncondensate densities in the vicinity of a vortex and to the geometrical arrangement of vortices in space.