Preparing Topological States of a Bose-Einstein Condensate

The burgeoning field of Bose-Einstein condensation in dilute alkali and hydrogen gases has stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems. The recent experiments offer the possibility for exploring fundamental properties of low temperature physics in a very controllable and accessible way. One current goal of experimenters in this field is to observe superfluid-like behavior in these trapped Bose gases, analogous to persistent currents in superfluid liquid helium, which flow without observable viscosity, and electric currents in superconductors, which flow without observable resistance. These ``super'' properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay due to thermal relaxation. Here we solve the time-dependent Gross-Pitaevskii equation of motion of the condensate involving two hyperfine atomic states and show how to generate, with extremely high fidelity, topological modes such as vortices that open the door to the study of superfluidity in these new systems. Our approach is inspired by recent experiments investigating a trapped condensate with two strongly coupled internal states. We show how the interplay between the internal and motional dynamics can be utilized to prepare the condensate in a variety of interesting configurations.