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arXiv · 0704.2315

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

A. Bermudez·M. A. Martin-Delgado·E. Solano
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Abstract

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.

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A. Bermudez, M. A. Martin-Delgado, E. Solano. 2007-04-18. Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal. https://doi.org/10.1103/physreva.76.041801

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