Finite-resolution fluctuation measurements of a trapped Bose-Einstein condensate.

We consider the fluctuations in atom number that occur within finite-sized measurement cells in a trapped Bose-Einstein condensate. These approximate the fluctuation measurements made in current experiments with finite-resolution in situ imaging. A numerical scheme is developed to calculate these fluctuations using the quasiparticle modes of a cylindrically symmetric three-dimensionally trapped condensate with either contact or dipole-dipole interactions. We use this scheme to study the properties of a pancake-shaped condensate using cylindrical cells. The extension of the theory to washer-shaped cells with azimuthal weighting is made and used to discriminate between the low-energy roton modes in a dipolar condensate according to their projection of angular momentum. Our results are based on the Bogoliubov approach valid for zero and small finite temperatures. [ABSTRACT FROM AUTHOR]