Atomic Bose-Einstein Condensation with Three-Body Interactions and Collective Excitations

TL;DR

This paper explores how three-body interactions influence the stability, collective excitations, and phase transitions of Bose-Einstein condensates, revealing that such interactions can significantly extend condensate lifetime and induce phase transitions.

Contribution

It introduces an extended Ginzburg-Pitaevskii-Gross equation incorporating three-body forces and analyzes their effects on condensate stability and collective modes.

Findings

Three-body interactions can increase the maximum number of condensed atoms.

A first-order liquid-gas phase transition occurs in the condensate.

The collective mode frequency depends on atom number and three-body force strength.

Abstract

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schr\"odinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest frequency of the collective mode is determined and its dependences on the number of atoms and on the strength of the three-body force are studied. We show that the addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We also observe a first-order liquid-gas phase transition for the condensed state up to a critical strength of the effective three-body force.