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We propose a measurement scheme that allows determination of even-moments ofa Bose-Einstein condensate (BEC) atom number, in a ring cavity, by continuousphotodetection of an off-resonant quantized optical field. A fast cavityphotocounting process limits the heating of atomic samples with a relativelysmall number of atoms, being convenient for BECs on a microchip scaleapplications. The measurement back-action introduces a counting-conditionedphase damping, suppressing the condensate typical collapse and revivaldynamics.Comment: Replaced with final published versio

Continuous measurement of atom-number moments of a Bose-Einstein condensate by photodetection