Kosterlitz-Thouless Transition in RF Dressed Ultra-Cold Gases

Very low temperature dilute trapped atomic gases form a well known state, the Bose-Einstein condensate (BEC). Recent work has made it possible to adiabatically transfer condensates from 3 dimensional traps into RF dressed traps that hold the atoms in a small region around a specific magnetic field. For a quadrupole magnetic trap, this results in an ”eggshell” potential, where atoms’ movement is very limited in the radial direction. The addition of gravity causes the atoms to form a simply connected disc at the bottom of the shell. This potential can be used as a test bed for two dimensional physics. In this paper, we will review the basics of the Kosterlitz-Thouless transition. The Kosterlitz-Thouless transition occurs when a two dimensional system with continuous symmetry moves from a quasi-ordered state to a disordered one by the creation of vortices. The transition will then be considered in the context of the two dimensional dilute gas mentioned above.