Phase space crystals: a new way to create a quasienergy band structure.

@article{Guo2013PhaseSC,
  title={Phase space crystals: a new way to create a quasienergy band structure.},
  author={Lingzhen Guo and Michael Marthaler and Gerd Sch{\"o}n},
  journal={Physical review letters},
  year={2013},
  volume={111 20},
  pages={
          205303
        }
}
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial periodicity, but it is driven by a time-dependent field coupling highly nonlinearly to one of its degrees of freedom (e.g., ∼q(n)). The band structure in quasienergy arises as a consequence of the n-fold discrete periodicity in phase space induced by this driving field… 

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