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We consider a small F=1 spinor condensate inside an optical cavity driven byan optical probe field, and subject the output of the probe to a homodynedetection, with the goal of investigating the effect of measurement back-actionon the spin dynamics of the condensate. Using the stochastic master equationapproach, we show that the effect of back-action is sensitive to not only themeasurement strength but also the quantum fluctuation of the spinor condensate.The same method is also used to estimate the atom numbers below which theeffect of back-action becomes so prominent that extracting spin dynamics fromthis cavity-based detection scheme is no longer practical.

Measurement back-action on the quantum spin-mixing dynamics of a spin-1 Bose-Einstein condensate