Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions

2002/10/10 by Rina Kanamoto, Hiroki Saito, Masahito Ueda · 10 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat

paper · pdf · doi:10.1103/physreva.67.013608

7 pages, 9 figures

arxiv created 2002/10/10 · openalex publication_date 2003/01/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by the recent development of the Feshbach technique, we studied the ground and low-lying excited states of attractive Bose-Einstein condensates on a one-dimensional ring as a function of the strength of interactions. The Gross-Pitaevskii mean-field theory predicts a quantum phase transition between a uniform condensate and a bright soliton, and a gapless singular cusp in the Bogoliubov excitation spectrum at the critical point. However, the exact diagonalization reveals the presence of an energy gap at the critical point, where the singularity is smeared by quantum fluctuations.

Citations

• Existence of Long-Range Order in One and Two Dimensions

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