Klein tunneling and Dirac potentials in trapped ions

@article{Casanova2010KleinTA,
  title={Klein tunneling and Dirac potentials in trapped ions},
  author={Jorge Casanova and Juan Jos{\'e} Garc{\'i}a-Ripoll and Rene Gerritsma and Christian F. Roos and Enrique Solano},
  journal={Physical Review A},
  year={2010},
  volume={82},
  pages={020101}
}
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scattering and Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the $1+1$ Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states… 

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References

SHOWING 1-10 OF 26 REFERENCES
Dirac equation and quantum relativistic effects in a single trapped ion.
TLDR
This work presents a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion, and studies relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrel ativistic limits, via the tuning of controllable experimental parameters.
Quantum simulation of the Dirac equation
TLDR
A proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states.
Exact mapping of the 2+1 Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal
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
Mesoscopic superposition states in relativistic Landau levels.
We show that a linear superposition of mesoscopic states in relativistic Landau levels can be built when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable
Simulating a quantum magnet with trapped ions
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We cannot translate quantum behaviour arising from superposition states or
The Dirac Equation
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all
Solution of the one-dimensional Dirac equation with a linear scalar potential
We solve the Dirac equation in one spatial dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817–818 (2001)] by
Geometric phase gate on an optical transition for ion trap quantum computation
We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric
Perturbation theory for metastable states of the Dirac equation with quadratic vector interaction
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The cases in one spatial dimension and in three
Klein paradox in spatial and temporal resolution.
Based on spatially and temporally resolved numerical solutions to the relativistic quantum field equations, we provide a resolution to the controversial issue of how an incoming electron scatters off
...
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