Bose-Einstein Condensation and strong-correlation behavior of phonons in   ion traps
  We show that the dynamics of phonons in a set of trapped ions interacting with lasers is described by a Bose-Hubbard model whose parameters can be externally adjusted. We investigate the possibility of observing several quantum many-body phenomena, including (quasi) Bose-Einstein condensation as well as a superfluid-Mott insulator quantum phase transition. 
D. Porras and J.I. Cirac