Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature

@article{Bissbort2016OperatorbasedDO,
  title={Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature},
  author={Ulf Bissbort and Walter Hofstetter and Dario Poletti},
  journal={Physical Review B},
  year={2016},
  volume={94},
  pages={214305}
}
We present a self-contained operator-based approach to derive the spectrum of trapped ions. This approach provides the complete normal form of the low energy quadratic Hamiltonian in terms of bosonic phonons, as well as an effective free particle degree of freedom for each spontaneously broken spatial symmetry. We demonstrate how this formalism can directly be used to characterize an ion chain both in the linear and the zigzag regimes. In particular we compute, both for the ground state and… 
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