Exact mapping of the2+1Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal

2007/04/18 by A. Bermúdez, A. Bermudez, M. A. Martín-Delgado +2 · 11 citations
Computer Science · Mathematics · Physics and Astronomy · #Discrete mathematics #Equivalence (formal languages) #Field (mathematics) #Ion #Mathematics #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum optics and atomic interactions #Zitterbewegung #quant-ph

paper · pdf · doi:10.1103/physreva.76.041801

published as Rap. Comm. PRA 76, 041801 (R) (2007) · Revtex4, submitted for publication

arxiv created 2007/04/18 · openalex publication_date 2007/10/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Comparison of quantum and semiclassical radiation theories with application to the beam maser
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Manipulating quantum entanglement with atoms and photons in a cavity
• Zitterbewegungof Electronic Wave Packets in III-V Zinc-Blende Semiconductor Quantum Wells

Cited by

• Hyperstatistical thermodynamics of the one-dimensional Klein-Gordon and Dirac oscillators: a closed-form q-generalized Boltzmann factor and a quantitative comparison with Beck's superstatistics
• Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction
• Quantum simulations with cold trapped ions
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• The study of the generalized Klein–Gordon oscillator in the context of the Som–Raychaudhuri space–time
• The DKP oscillator with a linear interaction in the cosmic string space-time
• Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems
• Благотворительность и ротарианство в России: взгляд извне
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Dirac oscillator in an external magnetic field
• Anomalous electron trajectory in topological insulators

Related

• Optical perspective on the time-dependent Dirac oscillator
• Zitterbewegung in Quantum Mechanics -- a research program
• More about the S=1 relativistic oscillator
• Jaynes-Cummings Model Dynamics in Two Trapped Ions
• Dirac oscillator in an external magnetic field