  The existence of a geometric phase in magnetic traps can be used to Bose
condense a magnetically trapped atomic gas into a vortex state. We propose an
experimental setup where a magnetic trap together with a blue detuned laser
beam form a multiply connected trap geometry. The local variation of the
magnetic quantization axis induces a geometric or Berry's phase that allows the
atoms to acquire an effective gauge charge interacting with the analog of a
magnetic solenoid. It is shown that the ground state of such a system may be
given by a vortex state. We also discuss the influence of atomic interactions
on the proposed vortex production scheme in the context of present
Bose-Einstein condensation experiments with dilute gases.
