We study the spin distribution and macroscopic entanglement in spinor condensates confined in an anisotropic potential under external magnetic fields. Different types of magnetic phases can be reached by tuning the magnetic dipolar interaction strength by modifying the trapping geometry. We investigate the atom-number fluctuations of the ground state and show that the different internal hyperfine states exhibit super-Poissonian, Poissonian, and sub-Poissonian distributions with different trapping geometries and strengths of the external magnetic field. We also propose a scheme to create a macroscopic maximally entangled spin state by slowly sweeping the external magnetic field.
We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap and find that the atom-number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms $N\ensuremath{\gtrsim}2$, we measure a reduction factor (Fano factor) of $0.72\ifmmode\pm\else\textpm\fi{}0.07$, which differs from 1 by more than four standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multiatom losses, leading to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of
3/4 for the Fano factor at large
N and in the steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.