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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 (BEC). This approximates 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 (DDIs). 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 pro- jection of angular momentum. Our results are based on the Bogoliubov approach valid for zero and small finite temperatures.