Geometric Resonances in Bose-Einstein Condensates with Two- and Three-Body Interactions

TL;DR

This paper explores geometric resonances in Bose-Einstein condensates with two- and three-body interactions, using analytical and numerical methods to analyze mode coupling, frequency shifts, and stability in anisotropic traps.

Contribution

It introduces a combined analytical and numerical approach to study nonlinear effects and stability in BECs with complex interactions, extending understanding of resonance phenomena.

Findings

Resonances depend on trap anisotropy and interaction strengths.

A small repulsive three-body interaction enhances condensate stability.

Analytical predictions match numerical simulations of mode shifts.

Abstract

We investigate geometric resonances in Bose-Einstein condensates by solving the underlying time-dependent Gross-Pitaevskii equation for systems with two- and three-body interactions in an axially-symmetric harmonic trap. To this end, we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)], based on both a perturbative expansion and a Poincar\'e-Lindstedt analysis of a Gaussian variational approach, as well as a detailed numerical study of a set of ordinary differential equations for variational parameters. By changing the anisotropy of the confining potential, we numerically observe and analytically describe strong nonlinear effects: shifts in the frequencies and mode coupling of collective modes, as well as resonances. Furthermore, we discuss in detail the stability of a Bose-Einstein condensate in the presence of an attractive two-body interaction and a repulsive three-body interaction. In particular, we show that a small repulsive three-body interaction is able to significantly extend the stability region of the condensate.