Collapse and revival of excitations in Bose-Einstein condensates

TL;DR

This paper investigates the energies and decay behaviors of elementary excitations in Bose-Einstein condensates at finite temperature, revealing negative energy shifts, collapse and revival phenomena, and explaining Beliaev decay experimentally observed.

Contribution

It introduces a finite-temperature gapless second-order theory to analyze excitation energies and decay, highlighting new effects like collapse and revival in low-lying modes.

Findings

High-lying collective modes have systematically negative energy shifts.

Low-lying modes exhibit collapse and revival decay effects.

Perturbation theory explains Beliaev decay of scissors mode.

Abstract

We study the energies and decay of elementary excitations in weakly interacting Bose-Einstein condensates within a finite-temperature gapless second-order theory. The energy shifts for the high-lying collective modes turn out to be systematically negative compared with the Hartree-Fock-Bogoliubov-Popov approximation and the decay of the low-lying modes is found to exhibit collapse and revival effects. In addition, perturbation theory is used to qualitatively explain the experimentally observed Beliaev decay process of the scissors mode.