Measurement theory and interference of spinor Bose-Einstein condensates

We study two aspects of measurement theory in spinor Bose-Einstein condensates of $F=1$ atoms: the probability of obtaining a certain outcome of the measurement and the evolution of the state of the condensate due to the measurement. We also study the interference patterns arising from the spatial overlap of two spinor condensates. We show that neither a measurement on a small number of escaping atoms nor an interference experiment can distinguish between an antiferromagnetic coherent state condensate, i.e., a condensate in which all the atoms have ${S}_{z}=0$ along an a priori unknown direction, and a spin-singlet condensate, i.e., a condensate with ${S}_{\mathrm{total}}=0.$ We also show that a singlet-state condensate evolves into a coherent state as a result of the measurement.