We describe schemes for transferring quantum states between light fields an
d the motion of a trapped atom. Coupling between the motion and the light i
s achieved via Raman transitions driven by a laser field and the quantized
field of a high-finesse microscopic cavity mode. By cascading two such syst
ems and tailoring laser held pulses, we show that it is possible to transfe
r an arbitrary motional state of one atom to a second atom at a spatially d
istant site.