We propose an all-quantized Jaynes-Cummings (JC) interaction between a
trapped ultracold ion with a quantized radiation held. The carrier ex
citation gives the usual JC model in cavity QED, but the red and blue
excitations will result in three-body interactions analogous to a two-
mode problem in quantum optics. (C) 1998 Published by Elsevier Science
B.V.