Crystalline boson phases in harmonic traps: Beyond the Gross-Pitaevskii mean field

TL;DR

This paper investigates strongly repelling bosons in two-dimensional harmonic traps, revealing crystalline phases and correlations beyond the Gross-Pitaevskii mean field, with implications for neutral and charged bosonic systems.

Contribution

It introduces a method combining symmetry breaking and restoration to incorporate correlations beyond the GP solution, revealing crystalline patterns in bosonic traps.

Findings

Bosons form polygonal-ring-like crystalline patterns.

Crystalline phase energy saturates and becomes more localized than GP condensate.

Charged bosons approach classical point-charge configurations.

Abstract

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.