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arXiv:cond-mat/0210640 · Physical Review A

Bose-Einstein condensates with attractive interactions on a ring

G. M. Kavoulakis

Published Jan 17, 2003• 54 citations
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Abstract

Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme, are used to attack the problem.

DOI
10.1103/physreva.67.011601

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Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the coupling constant increases. Both the mean-field approximation, as well as a diagonalization scheme, are used to attack the problem.
Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.
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.
We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov--de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime, three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state, and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.
We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.