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 1,2 . 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 3 . 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 4,5 . We show how the interplay between the internal and motional dynamics can be utilized to prepare the condensate in a variety of interesting configurations.Since 1995, when Bose-Einstein condensation in a dilute atomic gas was first observed 6−8 , experimenters have sought a method to create a vortex in this system. In a typical experiment, around one million atoms are trapped in a magnetic harmonic potential and cooled below the critical temperature so that condensation occurs into the lowest energy quantized mode. In the usual case, this ground state has no circulation. One proposed scheme for preparing the condensate in a vortex mode 9−17 is to distort the confining potential and mechanically rotate the trap during the cooling process. In this way, the lowest energy mode may be engineered to be circulating about the axis of symmetry. Such an approach is in direct analogy with experiments on vortices in superfluid helium-the asymmetry of the harmonic trap for the atomic gas plays the role of surface roughness of a rotating vessel. Although conceptually this method appears promising for vortex generation in a trapped gas, so far technical difficulties have precluded its successful implementation.Instead of having the system condense into a vortex mode, an alternative approach is to allow the atoms to condense into the usual ground state and then dynamically generate the vortex from the non-rotating condensate. Several theoretical proposals have been made along these lines which utilize the interaction between the atoms and a specific laser field consisting of a beam of photons with non-zero orbital angular momentum 18−20 .The method we present here makes use of both of the techniques mentioned-mechanical rotation and the coupling of internal states using an el...

We propose an experiment that would demonstrate nonlinear Josephson-type oscillations in the relative population of a driven, two-component Bose-Einstein condensate. An initial state is prepared in which two condensates exist in a magnetic trap, each in a different hyperfine state, where the initial populations and relative phase between condensates can be controlled within experimental uncertainty. A weak driving field is then applied, which couples the two internal states of the atom and consequently transfers atoms back and forth between condensates. We present a model of this system and investigate the effect of the mean field on the dynamical evolution.

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of 87 Rb.