Temperature Dependent Density Profiles of Dipolar Droplets

Recently, trapped dipolar gases were observed to form high density droplets in a regime where mean field theory predicts collapse. These droplets present a novel form of equilibrium where quantum fluctuations are critical for stability. So far, the effect of quantum fluctuations have only been considered at zero temperature through the local chemical potential arising from the Lee--Huang--Yang correction. Here, we extend the theory of dipolar droplets to non-zero temperatures using Hartree--Fock--Bogoliubov theory (HFBT), and show that the equilibrium is strongly affected by temperature fluctuations. HFBT, together with local density approximation for excitations, reproduces the zero temperature results, and predict that the condensate density can change dramatically even at low temperatures where the total depletion is small. Particularly, we find that typical experimental temperatures ($T \sim $ 100 nK) can significantly modify the transition between low density and droplet phases.