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Physical Review A

Many-body ground-state properties of an attractive Bose-Einstein condensate in a one-dimensional ring

A. Montina, F. T. Arecchi

Published Jun 27, 2005• 8 citations
Publisher

Abstract

We study a Bose-Einstein condensate with attractive interactions in a one-dimensional ring and show that the ground state is well described by the superposition of bright solitons. A position measurement of some atoms gives rise to the state reduction of the soliton position, which increases the condensate fraction. The bunched many-body ground state is well approximated by a simple variational wave function.

DOI
10.1103/physreva.71.063615

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We study a Bose-Einstein condensate with attractive interactions in a one-dimensional ring and show that the ground state is well described by the superposition of bright solitons. A position measurement of some atoms gives rise to the state reduction of the soliton position, which increases the condensate fraction. The bunched many-body ground state is well approximated by a simple variational wave function.
We study the ground-state properties of a one-dimensional Bose gas with NNN-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schr\"odinger equation, we compute the chemical potential and the ground-state energy. For N=3N=3N=3, a localized soliton wave function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parametrized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of NNN-body attractive contact interactions in higher dimensions is presented.
We study the properties of Bose-Einstein condensates in a one-dimensional ring with periodically modulated interaction strength. We demonstrate that within the semiclassical mean-field theory, a condensate can undergo a quantum phase transition between a solitonlike state and a spatially periodic condensate that matches the scattering length modulation. However, we show via exact diagonalization of the full many-body Hamiltonian that the solitonic ground states do not exist in the true quantum treatment. Instead, the system is driven into an entangled macroscopic-quantum-superposition-like state and the semiclassical soliton state may be regarded as a decohered macroscopic quantum superposition state. We investigate how the properties of the quantum ground state scales with the total number of atoms. Our work elucidates how semiclassical properties emerge from quantum behavior.
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.
The form and stability of quantum vortices in Bose-Einstein condensates with attractive atomic interactions is elucidated. They appear as ring bright solitons, and are a generalization of the Townes soliton to nonzero winding number m. An infinite sequence of radially excited stationary states appear for each value of m, which are characterized by concentric matter-wave rings separated by nodes, in contrast to repulsive condensates, where no such set of states exists. It is shown that robustly stable as well as unstable regimes may be achieved in confined geometries, thereby suggesting that vortices and their radial excited states can be observed in experiments on attractive condensates in two dimensions.