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

TL;DR

This paper investigates the critical fluctuations and symmetry-breaking phenomena in attractive Bose-Einstein condensates, revealing how weak perturbations induce soliton formation and affect condensate stability.

Contribution

It introduces an extended mean-field theory that accurately describes the transition from symmetric states to solitons in attractive BECs, aligning with exact diagonalization results.

Findings

Weak symmetry-breaking causes the transition to a bright soliton.

Center-of-mass fluctuations mainly come from condensate depletion.

Extended mean-field theory reproduces exact diagonalization results.

Abstract

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.