Interplay of higher-order quantum fluctuations and disorder in dipolar and nondipolar ultracold Bose gases

We study the impact of higher-order quantum, thermal fluctuations and disorder in three-dimensional ultracold Bose gases using the self-consistent Hartree-Fock-Bogoliubov theory. This method ensures a gapless excitation spectrum consistent with the Hugenholtz-Pines theorem. The disorder-induced condensate deformation feeds back into the quasiparticle spectrum allowing us to obtain higher-order corrections to the sound velocity, equation of state, condensed and superfluid densities for Bose-Einstein condensates with both short-range and an additional dipolar interaction. Our findings highlight the rich interplay between disorder, interaction, quantum, and thermal fluctuations which generates nontrivial effects in such systems. We show in particular that disorder and fluctuations can scatter particles out of the condensate strongly reducing the condensed fraction, while leaving enough long-range phase coherence for superflow. In the presence of dipolar interactions, the superfluid density displays an anomalous behavior due to the intriguing competition between anisotropy and higher-order corrections.