  We study the dynamics of the 2+1 Dirac oscillator exactly and find spin
oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We
find an exact mapping of this quantum-relativistic system onto a
Jaynes-Cummings model, describing the interaction of a two-level atom with a
quantized single-mode field. This equivalence allows us to map a series of
quantum optical phenomena onto the relativistic oscillator, and viceversa. We
make a realistic experimental proposal, at reach with current technology, for
studying the equivalence of both models using a single trapped ion.
