Crystalline phases of bosons in harmonic traps

Strongly repelling bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree- Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross- Pitaevskii (GP) solution. The bosons localize and form polygonal-ring-like crystalline patterns, both for a repulsive contact potential and a Coulomb interaction, as revealed via conditional-probability-distribution analysis. For neutral bosons, the total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate. For charged bosons, the total energy and dimensions approach the values of classical point-like charges in their equilibrium configuration. For neutral bosons, the present work describes a 2D generalization of the 1D Tonks-Girardeau regime of impenetrable bosons.\footnote{Phys. Rev. Lett. (Dec. 2004); cond-mat/0410598; to see a preprint \urllink{CLICK HERE}{http://arxiv.org/abs/cond- mat/0410598}}