Dipolar Bose-Einstein condensates at Finite temperature

We study a Bose-Einstein condensate (BEC) of a dilute gas with dipolar interactions, at finite temperature, using the Hartree-Fock-Bogoliubov (HFB) theory within the Popov approximation. An additional approximation involving the dipolar exchange interaction is made to facilitate the computation. We calculate the temperature dependence of the condensate fraction of a condensate confined in a cylindrically symmetric harmonic trap. We show that the bi-concave shaped condensates found in Ref. \cite{Ronen07} in certain pancake traps at zero temperature, are also stable at finite temperature. Surprisingly, the dip in the central density of these structured condensates is actually enhanced at low finite temperatures. We explain this effect.