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arXiv:cond-mat/9911089 · Journal of Physics B Atomic Molecular and Optical Physics

Atomic Bose-Einstein condensation with three-body interactions and collective excitations

A. Gammal, T. Frederico, Lauro Tomio, Ph. Chomaz

Published Sep 15, 2000• 127 citations
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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 Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. 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 study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.

DOI
10.1088/0953-4075/33/19/316

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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 Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. 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 study in detail the first-order liquid–gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter. 1.
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 Schrödinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s−s-s−wave. The lowest frequency of the collective mode is determined through the Fourier transform of the time dependent solution and its dependences on the number of atoms and 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 study the effects of a repulsive three-body interaction on a system of trapped ultra-cold atoms in a Bose-Einstein condensed state. The corresponding s−s-s−wave non-linear Schrödinger equation is solved numerically and also by a variational approach. A first-order liquid-gas phase transition is observed for the condensed state up to a critical strength of the effective three-body force.
We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schr\"odinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.
This paper investigates the collective excitation and stability of low-dimensional Bose–Einstein condensates with two- and three-body interactions by the variational analysis of the time-dependent Gross–Pitaevskii–Ginzburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate are obtained. The results show that: (i) the repulsive two-body interaction among atoms makes the frequency red-shifted for the internal excitation and the repulsive or attractive three-body interaction always makes it blue-shifted; (ii) the region for the existence of the stable bound states is obtained by identifying the critical value of the two- and three-body interactions.
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an sss-wave scattering length a<0a<0a<0 and a three-body scattering hypervolume D>0D>0D>0. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.