Quantum state transfer between motion and light

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