Spin Correlation and Discrete Symmetry in Spinor Bose-Einstein Condensates

Abstract

We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal $2$ channel. We show that the low energy spin dynamics in the system can be mapped into an $o\left(n\right)$ nonlinear sigma model. $n=3\mathrm{}$ at the zero magnetic field limit and $n=2\mathrm{}$ in the presence of weak magnetic fields. In an ordered phase, the ground state has a discrete $Z_2$ symmetry and is degenerate under the group $\left[U\right(1)\times S^{n-1\mathrm{}}]{/Z}_2$. We explore consequences of the discrete symmetry and propose some measurements to probe it.