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

Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal