Exact mapping of the 2+1 Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal

By A. Bermudez, Miguel Angel Martin-Delgado, Enrique Solano. 2007

170 citations recorded by the source corpus.

We study the dynamics of the $2+1$ Dirac oscillator exactly and find spin oscillations due to a 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 vice versa. We make a realistic experimental proposal, in reach with current technology, for studying the equivalence of both models using a single trapped ion.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d15494507f79bf10142f1e36ae2441235ae7132d

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum simulations with cold trapped ions (2009, methodology): “MethodsRelativistic effects related to the solution of the Dirac equation can be simulated in trapped ions systems as proposed in [Bermudez et al. 2007] and [Lamata et al. 2007], in particular phenomena like theZitterbewegung(helicoidal motion of the free Dirac particle as a consequence of the…”
Quantum Simulation (2013, methodology): “…2006b), quantum chaos (Howell and Yeaze, 2000; Weinstein et al., 2002), some simple chemical reactions (Smirnov et al., 2007), Dirac particles (Bermudez et al., 2007; Gerritsma et al., 2010; Lamata et al., 2007), the Unruh effect (Alsing et al., 2005; Nation et al., 2012), or anyons (Lu et…”
Quantum simulation of the Dirac equation (2009, background): “Furthermore, the mapping between quantum optical systems and relativistic quantum mechanics may be followed by further analogies between the Dirac dynamics and the Jaynes-Cummings model [9, 28, 29] and photonic [10] or sonic analogies [30].”