  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.
