Atomic-number fluctuations in a mixture of condensates

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction c(12)beta is adjusted. The two spin-1 condensates forming the mixture are, respectively, ferromagnetic and polar in the absence of an external magnetic (B) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when c(12)beta > 0), where the ground state becomes fragmented and atomic-number fluctuations exhibit drastically different features from a single standalone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.