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

We consider a small F=1 spinor condensate inside an optical cavity driven by an optical probe field, and subject the output of the probe to a homodyne detection, with the goal of investigating the effect of measurement backaction on the spin dynamics of the condensate. Using the stochastic master equation approach, we show that the effect of backaction is sensitive to not only the measurement strength but also the quantum fluctuation of the spinor condensate. The same method is also used to estimate the atom numbers below which the effect of backaction becomes so prominent that extracting spin dynamics from this cavity-based detection scheme is no longer practical.