Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates

Details Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates

2005-11-29

arxiv.org/abs/cond-mat/0511684v3

Phys. Rev. A 73, 033611 (2006)

Physics

Condensed Matter

Other Condensed Matter

14 pages, 13 figures

Scientific paper

10.1103/PhysRevA.73.033611

We employ mean-field, Bogoliubov, and many-body theories to study critical fluctuations in position and momentum of a Bose-Einstein condensate whose translation symmetry is spontaneously broken due to attractive interactions. In a homogeneous system, the many-body ground state of the symmetry-preserving Hamiltonian is very fragile against superposition of low-lying states, while mean-field theory predicts a stable bright soliton which spontaneously breaks translation symmetry. We show that weak symmetry-breaking perturbations cause the translation-symmetric many-body ground state to cross over to a many-body bright soliton. We argue that the center-of-mass fluctuations in the soliton state arise primarily from the depletion of the condensate to translation modes. We develop an extended mean-field theory to analytically reproduce these results obtained by the exact diagonalization method.

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