Effects of temperature upon the collapse of a Bose-Einstein condensate in a gas with attractive interactions

Abstract

We present a study of the effects of temperature upon the excitation frequencies of a Bose-Einstein condensate formed within a dilute gas with a weak attractive effective interaction between the atoms. We use the self-consistent Hartree-Fock Bogoliubov treatment within the Popov approximation and compare our results to previous zero temperature and Hartree-Fock calculations The metastability of the condensate is monitored by means of the $l=0$ excitation frequency. As the number of atoms in the condensate is increased, with $T$ held constant, this frequency goes to zero, signalling a phase transition to a dense collapsed state. The critical number for collapse is found to decrease as a function of temperature, the rate of decrease being greater than that obtained in previous Hartree-Fock calculations.