The absence of fragmentation in Bose-Einstein condensates

TL;DR

This paper discusses how symmetries in Hamiltonians lead to fragmented Bose-Einstein condensates, but weak symmetry-breaking perturbations favor unfragmented states, impacting experimental realizations.

Contribution

It demonstrates that symmetry considerations cause fragmentation in Bose-Einstein condensates and shows how small perturbations favor unfragmented states, clarifying experimental challenges.

Findings

Symmetry causes fragmentation in Bose-Einstein condensates.

Weak symmetry-breaking perturbations destabilize fragmented states.

Unfragmented condensates are more likely in realistic conditions.

Abstract

A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or translationally symmetric is fragmented as a direct result of these symmetries. A corresponding mean-field unfragmented state, with an identical energy to leading order in the number of particles, can generally be constructed. As a consequence, vanishingly weak symmetry-breaking perturbations destabilize the fragmented state, which would thus be extremely difficult to realize experimentally, and lead to an unfragmented condensate.