Temperature dependent density profiles and collective oscillations of dipolar droplets

Abstract

Dipolar droplets are a novel form of Bose gas that form in a regime where the mean field theory predicts collapse. In the literature, the beyond mean field e ects in the form of the Lee-Huang-Yang correction to the local chemical potential are used to explain the stability of these droplets. We employ the Hartree-Fock- Bogoliubov theory to include the beyond mean field terms in a systematic manner that also allows finite temperature calculations. In this thesis, we derive the modified Gross-Pitaevskii equation and the Bogoliubov-de Gennes equations, then solve the latter with a local density approximation and the former with a Gaussian variational anzats. We show that Hartree-Fock-Bogoliubov theory reproduces the zero temperature results found in the literature, and indicates that the density profile and the collective oscillation of dipolar droplets depend on the temperature. We find that experimentally relevant temperatures (T 100nK) may significantly alter the transition between low and high density phases, and change the collective oscillation frequencies of the system.