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We study particle number fluctuations in the quantum ground states of amixture of two spin-1 atomic condensates when the interspecies spin-exchangecoupling interaction $c_{12}\beta$ is adjusted. The two spin-1 condensatesforming the mixture are respectively ferromagnetic and polar in the absence ofan external magnetic (B-) field. We categorize all possible ground states usingthe angular momentum algebra and compute their characteristic atom numberfluctuations, focusing especially on the the AA phase (when $ c_{12}\beta >0$),where the ground state becomes fragmented and atomic number fluctuationsexhibit drastically different features from a single stand alone spin-1 polarcondensate. Our results are further supported by numerical simulations of thefull quantum many-body system.

Atomic number fluctuations in a mixture of two spinor condensates