Normal form expansions and thermal decay rates of Bose-Einstein condensates with short- and long-range interaction

TL;DR

This paper develops a normal form expansion method to analyze the decay rates of Bose-Einstein condensates with short- and long-range interactions, providing detailed insights into their transition states and decay mechanisms at finite temperature.

Contribution

It introduces a variational normal form expansion approach to characterize transition states and decay rates of Bose-Einstein condensates with various interactions, including dipolar effects.

Findings

Normal form expansions accurately describe transition states.

Decay rates depend on the scattering length and interaction type.

Convergence of the normal form improves with extended Gaussian variational methods.

Abstract

The thermally induced coherent collapse of Bose-Einstein condensates at finite temperature is the dominant decay mechanism near the critical scattering length in condensates with at least partially attractive interaction. The collapse dynamics out of the ground state is mediated by a transition state whose properties determine the corresponding decay rate or lifetime of the condensate. In this paper, we perform normal form expansions of the ground and the transition state of condensates with short-range scattering interaction as well as with anisotropic and long-range dipolar interaction in a variational framework. This method allows one to determine the local properties of these states, i.e. their mean-field energy, their normal modes, the coupling between different modes, and the structure of the reaction channel to any desired order. We discuss the physical interpretation of the transition state as a certain density distribution of the atomic cloud and the behavior of the single normal form contributions in dependence on the s-wave scattering length. Moreover, we investigate the convergence of the local normal form when using extended Gaussian variational approaches, and present the condensate's decay rate.